After an unexpectedly strong showing on Tuesday night, Republicans are heading into the 2022 midterm elections with what they believe will be a highly effective political strategy capitalizing on the frustrations of suburban parents still reeling from the devastating fallout of pandemic-era schooling.

Seizing on education as a newly potent wedge issue, Republicans have moved to galvanize crucial groups of voters around what the party calls “parental rights” issues in public schools, a hodgepodge of conservative causes ranging from eradicating mask mandates to demanding changes to the way children are taught about racism.

Yet it is the free-floating sense of rage from parents, many of whom felt abandoned by the government during the worst months of the pandemic, that arose from the off-year elections as one of the most powerful drivers for Republican candidates.

Across the country, Democrats lost significant ground in crucial suburban and exurban areas — the kinds of communities that are sought out for their well-funded public schools — that helped give the party control of Congress and the White House. In Virginia, where Republicans made schools central to their pitch, education rocketed to the top of voter concerns in the final weeks of the race, narrowly edging out the economy.

The message worked on two frequencies. Pushing a mantra of greater parental control, Glenn Youngkin, the Republican candidate in Virginia, stoked the resentment and fear of some white voters, who were alarmed by efforts to teach a more critical history of racism in America. He attacked critical race theory, a graduate school framework that has become a loose shorthand for a contentious debate on how to address race. And he released an ad that was a throwback to the days of banning books, highlighting objections by a white mother and her high-school-age son to “Beloved,” the canonical novel about slavery by the Black Nobel laureate Toni Morrison.

But at the same time, Mr. Youngkin and other Republicans tapped into broader dissatisfaction among moderate voters about teachers’ unions, unresponsive school boards, quarantine policies and the instruction parents saw firsthand during months of remote learning. In his stump speeches, Mr. Youngkin promised to never again close Virginia schools.

While Terry McAuliffe, the Democratic nominee, and his party allies eagerly condemned the ugliest attacks by their opponents, they seemed unprepared to counter the wider outpouring of anger over schools.

For weeks before the Virginia election, Republicans pointed to the school strategy as a possible template for the entire party. Mr. Youngkin’s narrow but decisive victory on Tuesday confirmed for Republicans that they had an issue capable of uniting diverse groups of voters. The trend was most evident in Mr. Youngkin’s improvement over former President Donald J. Trump’s performance in the Washington suburbs, which include a mix of communities with large Asian, Hispanic and Black populations.

Representative Kevin McCarthy, the House majority leader, listed education as a main plank of his party’s plan to reclaim power, with promises to introduce a “Parents’ Bill of Rights.”

“If the Virginia results showed us anything, it is that parents are demanding more control and accountability in the classroom,” he wrote in an election-night letter to his caucus.

Steven Law, the president of American Crossroads, one of the most active outside groups working to elect Republicans to the House and Senate, said the strategy was ripe for replicating in races across the country.

“It’s always possible to overdo something,” he added, cautioning that Republicans would be unwise to pursue attacks that appear hostile to teachers themselves. “But very clearly there’s a high level of concern among parents over political and social experimentation in schools that transcends ideology.”

While the conservative news media and Republican candidates stirred the stew of anxieties and racial resentments that animate the party’s base — thundering about equity initiatives, books with sexual content and transgender students on sports teams — they largely avoided offering specific plans to tackle thornier issues like budget cuts and deepening educational inequalities.

But the election results suggested that Republicans had spoken about education in ways that resonated with a broader cross-section of voters.

In Virginia, the Youngkin campaign appealed to Asian parents worried about progressive efforts to make admissions processes in gifted programs less restrictive; Black parents upset over the opposition of teachers’ unions to charter schools; and suburban mothers of all races who were generally on edge about having to juggle so much at home over the last year and a half.

“This isn’t partisan,” said Jeff Roe, the Youngkin campaign’s chief strategist. “It’s everyone.”

Democrats largely declined to engage deeply with such charged concerns, instead focusing on plans to pump billions into education funding, expand pre-K programs and raise teacher pay.

In Virginia and New Jersey, the Democratic candidates for governor adopted the approach of Gov. Gavin Newsom of California, who faced a recall challenge that exploited similar lines of attack but beat it back by leaning into vaccination and mask mandates in schools.

Ahead of the midterms, many of the educational issues are sure to linger.

Already, the effects of remote learning on parents have been severe: School closures drove millions of parents out of the work force, led to an increase in mental health problems among children and worsened existing educational inequalities. Many of those effects were borne most heavily by key parts of the Democratic base, including women and Black and Latino families.

Strategists, activists and officials urged Democrats to prepare for the Republican attacks to be echoed by G.O.P. candidates up and down the ticket.

Geoff Garin, a top Democratic pollster, said the party’s candidates needed to expand their message beyond their long-running policy goals like reducing class sizes and expanding pre-K education.

“It’s going to be incumbent on Democrats to have a compelling response,” said Mr. Garin, who worked as a pollster for Mr. McAuliffe during his 2013 campaign for governor. “They also need to be prepared to assert the value of public education in terms of a place where there’s a common curriculum and common set of values that most voters agree are the right ones for public schools.”

Katie Paris, a party activist who runs Red, Wine and Blue, a group that works to mobilize suburban women, said that even as she warned that attacks over critical race theory had been “spreading like wildfire,” her pleas for resources had gone largely unanswered by party donors and officials.

“These outside forces have come for our schools and our communities, and at the highest levels within the Democratic Party, people have just said, ‘Well, don’t talk about it,’” she said. “The unwillingness to engage in this was a big mistake, and it will be in 2022, too.”

Rashad Robinson, the president of the racial justice organization Color of Change, expressed a similar concern, saying that Democrats’ reluctance to defend the need for public schools to teach honestly about race had left the party at a disadvantage.

Democrats, he said, “don’t show up when the conversation gets tough.”

“Critical race theory isn’t being taught, but we need to actually tell people what is being taught and why this is a strategy to prevent our kids from learning about all of our history,” said Mr. Robinson, who has advised Democratic strategists and candidates about their messaging on the issue. “It’s about banning Black history, but it’s also about banning American history.”

The issue, some party strategists admitted, is particularly complicated for Democrats who rely on teachers’ unions for financial and volunteer support. National and state union leaders drew public ire for slowing the reopening of schools even after teachers were given early access to vaccines. In the final days of the Virginia campaign, Mr. McAuliffe appeared with Randi Weingarten, the influential president of the American Federation of Teachers, which drew rebukes from Republicans.

After the election, Ms. Weingarten blamed Mr. McAuliffe’s defeat on his comment that he did not believe “parents should be telling schools what they should teach.” But she also chided Democrats for their timidity, warning that tough conversations were needed to rebuild trust between parents and their schools.

There are signs of limitations to the Republican approach. Though the party poured outside money and advertising into school board races — typically sleepy local affairs — the early results were mixed, with conservative candidates losing in Wisconsin, Connecticut and Minnesota.

Yet nationally, the issue seems particularly resonant in affluent suburban communities that faced some of the longest periods of remote schooling. While schools are universally open this year, education in Virginia and nationwide has continued to be disrupted by occasional quarantines and classroom closures to contain the coronavirus.

Last year, Virginia was among the East Coast states that were slowest to reopen schools for full-time, in-person learning. While some parents supported the cautious approach — driven by teachers’ unions, school boards and some administrators — others became frustrated and angry, especially in suburban counties like Fairfax and Arlington.

“There’s a level of anxiety and anger and people wanting to have their lives back,” said Ms. Weingarten, who faced blowback for hosting a town hall event in September with Open Schools USA, a group that opposes masks and vaccine mandates in schools. “But we have to engage. That, I think, is the big lesson.”

Dana Goldstein contributed reporting.