FOXBORO — It took three quarters, but the MVP candidate who led the Patriots back to the playoffs arrived in time Sunday to send them to the AFC Championship Game.

Drake Maye hit a 32-yard touchdown pass to Kayshon Boutte in the fourth quarter for the final score in a 28-16 divisional-round win over the Texans, a highlight-reel play that may live forever in playoff franchise lore. Maye’s touchdown survived a replay review and all but ended Houston’s hopes of survival in a game that otherwise played out as a defensive slugfest. He finished 16-of-27 for 179 yards, three touchdowns and an interception against the AFC’s best defense, which sacked him five times.

Maye fumbled on four of those five sacks, roadblocks the Texans threw on the Patriots’ path to victory. Pats coach Mike Vrabel credited his young quarterback for overcoming those mistakes to lead a winning effort.

“We talk about not going in the blender, and I think it’s hard,” Vrabel said. “They put pressure on us, and we know we’ve got to take care of the ball. Drake knows that. But to be able to stay the course and to trust Kayshon and give him a great ball that was (for) him or nobody — and those guys have kind of done that all year — when we needed a play, they’ve been able to do that for us.”

Maye admitted the snowy weather conditions affected his performance. It was an atypically inaccurate showing for Maye, who threw a few passes with no chance of being caught. He also fumbled three times in the first half but didn’t inflict any harm with his interception, a harmless Hail Mary before halftime.

Maye did have his moments, starting with a 28-yard touchdown to DeMario Douglas in the first quarter on fourth-and-1. Later, he ripped a 7-yard touchdown to Stefon Diggs to beat airtight coverage for a 21-10 lead late in the second quarter. As a runner, Maye had one scramble for eight yards.

“I think the biggest thing is getting back there with snow and just having a good grip on it and letting it rip,” Maye said. “The weather is no excuse, but there’s definitely times when the ball rolls around on the ground with the center before the snap, it gets a little wet. So it’s definitely tough, but I thought we made enough throws.”

Patriots veterans said Maye remained upbeat through his turnovers. Sunday was the second straight game where he’s thrown a second-half touchdown pass to pull away with a playoff win, having found tight end Hunter Henry for a 28-yard score in the fourth quarter of the Pats’ 16-3 Wild Card triumph over the Chargers.

“I think he’s learning that fast: how hard it is (in the playoffs) and how you just have to stay in the game,” Henry said. “Nothing’s going to be perfect, but you have to continue to fight, to scratch, to claw. Some things might not go your way, and you just have to come back and keep swinging.”

Maye is now 33-of-56 for 447 yards, four touchdowns, two interceptions and 10 sacks this postseason.