In the final hours of campaigning on Monday to become Virginia’s next governor, it was Glenn Youngkin offering an optimistic vision for the future while Terry McAuliffe delivered harsh warnings about ghosts of the past.

As the two men barnstormed across the state, the contrast in tone demonstrated their shifting fortunes in the highest profile race on the ballot on Tuesday. Mr. McAuliffe, a longtime fixture of the Democratic establishment, was scrambling to prevent President Biden’s unpopularity, the gridlock in Washington and Mr. Youngkin’s effective weaponizing of racial issues in the public schools from dooming his bid for a second term as governor.

Mr. Youngkin, for his part, was aiming to redefine how Republicans could win elections with former President Donald J. Trump out of the White House. He has accepted Mr. Trump’s support and has abstained from criticizing him, but Mr. Youngkin has kept Mr. Trump from visiting Virginia and never invokes his name during his stump speeches. A former private equity executive, Mr. Youngkin embraced Mr. Trump during the primary contest this year but spent the months since winning the Republican nomination keeping a rhetorical distance.

On Monday, in the Richmond area, Mr. Youngkin said he would lead a sweep of Republican victories across the state that would define a new era for the party — one that he has centered on giving parents greater control over the curriculum in public schools, particularly in how children are educated about racism.

“We will not teach our children to view everything through the lens of race,” Mr. Youngkin told supporters at a midday rally in an airplane hangar. “So on Day 1, I will ban critical race theory from Virginia’s schools.”

That theory, a graduate-level academic framework that argues that historical patterns of racism are ingrained in law and other modern institutions, is not taught in Virginia’s public schools. But conservatives have turned it into a flash point in key suburban areas such as Loudoun County, just outside Washington.

Earlier, in Roanoke, the biggest city in the mountain-specked southwest corner of the state, and a Republican stronghold, Mr. Youngkin promised voters that the party’s renewal was at hand.

“We’re going to have a whole new crop of Republicans come in and define a new way forward,” he told supporters in a morning rally at the airport.

While Mr. Youngkin never mentioned Mr. Trump in his 22-minute speech, he touched on several of the former president’s themes and deployed some of his catchphrases.

“I am so tired of Virginia losing,” Mr. Youngkin said. “I want Virginia to start winning again.”

Mr. Trump, who arranged to speak to his own Virginia supporters on Mr. Youngkin’s behalf during a Monday evening conference call “tele-rally,” appeared to be angling to take credit if Mr. Youngkin was victorious.

The media, Mr. Trump said in a statement earlier in the day, was “trying to create an impression that Glenn Youngkin and I are at odds and don’t like each other.” He said that this was untrue: “We get along very well together and strongly believe in many of the same policies.”

Still, Mr. Youngkin let it be known that he was too busy campaigning to attend the Trump call-in.

Mr. McAuliffe, crisscrossing the state in another plane, hammered away at the Trump-Youngkin connection, as he has for weeks. He warned that a victory by Mr. Youngkin would pave the way for Mr. Trump to attempt his own political restoration, and urged Virginians not to let the two of them exploit the state that way.