Next up is Baltimore, which stunned top-seeded Denver in double overtime Saturday, and lost 23-20 at Gillette Stadium last January in the last step before the Super Bowl. But the Ravens beat the Patriots in Week 3 this season at Baltimore.
Seldom-used Shane Vereen scored three times, twice on pinpoint throws from Brady, as New England (13-4) beat Houston (13-5) for the second time in a month.
Brady was missing some key helpers but got the usual outstanding performance from Wes Welker, his favorite target the last six years. The AFC's top receiver with 118 catches this season, Welker looked like he might reach that total against Houston's befuddled defense. He caught six in the first half for 120 yards, including a 47-yarder, and wound up with 8 for 131.
And the AFC East champion Patriots got more than anyone could have predicted from third-string running back Vereen, who scored their first two TDs on a 1-yard run and an 8-yard pass. He capped his biggest pro performance with an over-the-shoulder 33-yard catch early in the fourth period.
It was Brady's 41st postseason TD pass, behind only Brett Favre (44) and, you guessed it, Montana (45).
Nice company to be keeping.
"I grew up a 49ers fan," Brady said after throwing for three touchdowns in the AFC divisional playoff. "Joe Montana and Steve Young ... those guys are in another class."
The boost from Vereen offset the loss of tight end Rob Gronkowski, who broke his previously injured left arm and will require season-ending surgery, and RB Danny Woodhead (thumb) in the first quarter.
"Shane had a great game, just a huge growing up moment for him, very special," Brady said. "There were a lot of guys who made a lot of plays."
New England's defense helped put away the Texans. Rob Ninkovich's leaping third-quarter interception stopped a drive, and six plays later, Brady hit Brandon Lloyd for a 6-yard score.
Although the Texans got two fourth-quarter TDs on passes by Matt Schaub, their season ended with four defeats in their last six games. That slump cost the AFC South champions the top seed in the playoffs, forcing a trip to New England after they beat Cincinnati in the wild-card round.
The Texans couldn't measure up.
"Whenever the season ends, no matter when, it's really hard," tight end Owen Daniels said. "The farther along you get, the harder it is to take. It's one we wanted to win really bad. It's tough to swallow ... but one team gets to have a smile on their face at the end of the season, and it's not us this year."
Unlike their 42-14 loss here a month ago, the Texans didn't fold early. J.J. Watt, their dominating defensive end, bothered Brady, and when they fell behind 17-3, they had the fortitude to climb back.
But the Patriots pulled away in the third quarter for coach Bill Belichick's 17th postseason win, third behind Tom Landry (20) and Don Shula (19).
R New England quarterback Tom Brady wins his NFL-record 17th postseason game.
• Third-string Pats running back Shane Vereen scores three touchdowns one on the ground and two in the air.