MIAMI GARDENS, Fla. — The first turnover came on the Houston Texans’ opening drive. Quarterback Tyrod Taylor, pressured by Miami Dolphins safety Brandon Jones, lofted the ball to the end zone, and it landed in the rookie Jevon Holland’s hands for an interception.

From there, the Texans and the Dolphins swapped one puzzling giveaway after another: a poor decision by Dolphins quarterback Jacoby Brissett in the first quarter; three lost fumbles by the Dolphins (two by halftime); an attempted throwaway by Taylor that was turned into a sideline interception; back-to-back interceptions in the opening minutes of the third quarter; a late Houston fumble.

There were nine turnovers combined. It was ugly, even for teams that entered the matchup with only two combined wins. The Dolphins (2-7), with an impressive defensive performance and an offense led by Brissett after the regular starter, Tua Tagovailoa, was a late scratch because of a fractured finger on his throwing hand, did enough to eke out a 17-9 win at home.

“Not going to lie: It’s been a while,” Dolphins safety Eric Rowe said with a grin after the game.

Here were two teams with meager playoff aspirations, both without a win since Week 1, connected by trade rumors that started in the off-season when Miami was reportedly looking into trading for Houston quarterback Deshaun Watson.

Watson requested a trade out of Houston in January after expressing his discontent with not being involved in the team’s personnel decisions, including the hiring of General Manager Nick Caserio.

Less than two months after Watson’s trade request, the first of 22 civil lawsuits was filed against him by women who accused the quarterback of coercive and lewd sexual behavior. And neither the N.F.L. nor the Texans have shown that they know how to respond to a situation that has been one of the most prominent stories of the 2021 season.

Watson remains in a precarious spot on Houston’s roster. He has not suited up for a game this season, but he remains on the active roster. The presumption is that he has played his final game in a Texans uniform.

Houston (1-8), with one of the most porous rosters in the league, had conversations with the Dolphins ahead of Tuesday’s trade deadline, sparking speculation that the teams might reach some sort of agreement. Those talks fizzled as the deadline passed. The Dolphins owner Stephen M. Ross made clear his stipulation that Watson would need to resolve his legal matters before any trade. That, of course, was unlikely to happen by November.

Watson will remain with the Texans at least until the new league year begins in March 2022.

The Dolphins, a franchise trapped in a revolving door of poor drafting and instability, thought Watson, one of the best quarterbacks in the N.F.L. since entering the league, might be the missing piece to bolster their offense after Tagovailoa, whom Miami drafted fifth overall last year, has not taken the leap the team hoped he would.

Miami flipped a 5-11 record in 2019 to 10-6 last year, and the next step in the rebuild was clear: Get to the playoffs.

But after seven consecutive losses sandwiched between wins in Week 1 and on Sunday, the Dolphins are all but out of playoff contention and likely to miss the playoffs for the fifth straight season.

Tagovailoa, who was 6-3 as a starter last year, has missed four games this season, including three with a rib injury. In the off-season, Miami signed the former Texan Will Fuller and selected Jaylen Waddle, Tagovailoa’s teammate at Alabama, with the sixth pick in the draft, hoping to give the team speedier receiving options to go with DeVante Parker and tight end Mike Gesicki.

None of it has panned out, and before a five-sack outing against Houston, even Miami’s defense, which led the league in takeaways (29) in 2020, appeared to be regressing.

Week after week, Tagovailoa, has fielded questions about his status with a team that has been actively searching for his potential replacement. The Dolphins have mostly eluded questions about their interest in Watson.

“Tua is our quarterback,” Coach Brian Flores has repeated.

“I don’t not feel wanted,” Tagovailoa told reporters in October after again being asked if he felt the team was committed to him as Watson trade talks escalated.

“I actually think what the Dolphins did was smart,” said Mike Tannenbaum, a former executive vice president for football operations with the Dolphins. He later added: “I think getting to know him now is just being smart and proactive. And if at some point you don’t feel like it’s the appropriate thing to do, you could always walk away.”

In 2008, Tannenbaum, then the Jets’ general manager, traded for the 16-year Green Bay Packers quarterback Brett Favre, ending the tenure of Chad Pennington, who had been with the Jets since 2000.

“We had to go look Chad in the eye and say, ‘Yeah, these rumors are true, and as much as we like you, we think we have a chance to get better,’” Tannenbaum said in an interview. “And those are hard conversations, but to me, candidly, they’re appropriate. And we were a better team with Brett Favre.”

Similarly, Tannenbaum said, the Dolphins’ interest in Watson is a reflection of a leaguewide practice in which quarterbacks are constantly being evaluated, scrutinized and compared to other options. This situation, he added, just happens to be unfolding at a grander scale.

“We’re in the ultimate meritocracy,” Tannenbaum said. “So Tua should not just be worrying about Deshaun Watson rumors, he should be worrying about playing great. Because if he plays great, nothing else matters.”