The Patriots and Ravens will be meeting for the AFC title for the second straight year. Baltimore, which stunned top-seeded Denver in double overtime Saturday, lost 23-20 at Gillette Stadium last January.
Houston (13-5) performed far better than in a 42-14 loss here last month. But the Texans couldn't slow down Brady.
The Patriots overcame a 94-yard return by Danieal Manning on the opening kickoff thanks to Brady and Vereen and led 31-13 after three quarters.
Shayne Graham kicked a 55-yard field goal on the final play of the first half after a short punt by Zoltan Mesko gave the Texans the ball at their 38-yard line. That cut the lead to 17-13.
But the Patriots (12-4) scored on two of their three series in the third quarter on an 8-yard run by Stevan Ridley and a 5-yard pass from Brady to Brandon Lloyd.
The Patriots got little help from running back Danny Woodhead and tight end Rob Gronkowski, who left with injuries.
Woodhead hurt his thumb after carrying the ball on the Patriots' first offensive play and Gronkowski went to the locker room with an arm injury midway through the period. Gronkowski was playing his second game since breaking his left forearm.
After the Patriots took a 24-13 lead with Ridley's touchdown, both teams punted before the Texans started a drive at their 10. They moved to the New England 37 with the help of a 22-yard completion from Matt Schaub to Andre Johnson. But five plays later, Rob Ninkovich jumped and intercepted a pass over the middle intended for James Casey.
That gave the Patriots the ball at their 37 and they needed just six plays to score on Lloyd's touchdown in the first playoff game of his 10-year career.
Vereen had scored on a 1-yard run with 1:28 left in the first quarter after Graham opened the scoring with a 27-yard field goal.
Stephen Gostkowski gave the Patriots a 10-3 lead with a 31-yard field goal on the first series of the second quarter. They went ahead 17-3 as Brady threw to a wide-open Vereen, who easily ran into the end zone for an 8-yard touchdown reception.
But the Texans made it 17-10 with 1:15 left in the half on a 1-yard run by Arian Foster, who gained all 47 yards on the drive on five rushes. Manning had set them up with another big kickoff return. He ran 35 yards before being horse-collared by Gostkowski, who was called for a 15-yard penalty.
Manning's first kickoff return set up Graham's opening field goal just 1:03 into the game.
The Patriots punted on their first two possessions before taking charge.
After a poor punt by Donnie Jones gave them the ball at their 35, Ridley rushed 14 yards on the first play, then lost 2 on the next. Brady then connected on three straight passes: 13 yards to Ridley, 25 to Vereen and 14 to Aaron Hernandez.
Vereen ran in from the 1-yard line on the next play.
After Gostkowski's field goal, Jones punted again for Houston and New England started at its 20. With a second-and-3 at the Patriots 39, Brady hit Wes Welker for a 47-yard completion down the left sideline. It was Welker's 59th postseason catch, a New England club record, and he had 131 yards receiving on eight catches after three quarters.
On the next play, Vereen drifted out to the left with no Texan nearby and scored 3:38 before intermission.
The Patriots had early troubles on offense, punting on their first two possessions. Brady was sacked once, with NFL sacks leader J.J. Watt and Brooks Reed sharing credit for it.
In the first meeting with the Texans, Brady threw three touchdown passes on the Patriots' first three possessions.
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