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.
The winner of Sunday's game will host the Baltimore Ravens in the AFC championship game next Sunday.
New England's victory over Houston in Foxborough on Dec. 10 began the Texans' stretch of three losses in their last four regular-season games that cost them a playoff bye and home-field advantage.
But Houston beat the Cincinnati Bengals 19-13 in a wild-card game to advance to Sunday's rematch, the first playoff meeting between the Texans and Patriots.
AFC East champion New England had a first-round bye and is the top remaining AFC seed after the No. 1 Denver Broncos lost to the No. 4 Ravens 38-35 in double overtime on Saturday.
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