Lloyd scored just six plays after Rob Ninkovich ended a Houston threat with an interception that gave New England the ball at its 37-yard line.
The Patriots needed just one play after taking over on downs early in the fourth quarter, scoring on an outstanding over-the-shoulder catch by Vereen for a 33-yard touchdown and a 38-13 advantage.
The third-string back finished with 124 total yards — 83 on five receptions and 41 on seven carries.
"I don't come into the game knowing how much anyone is going to play," Vereen said. "I come into the game ready to go."
The Texans were.
On the very first play, Danieal Manning returned the kickoff 94 yards before being hauled down by Devin McCourty at the Patriots 12. But all the Texans could get out of that was a 27-yard field goal by Shayne Graham.
"That was a huge play by Devin to really end up saving (four) points," Belichick said.
The Patriots punted on their first two series then took the lead for good on Vereen's 1-yard run following Brady's consecutive completions of 13 yards to Ridley, 25 to Vereen and 14 to Aaron Hernandez.
The Texans offense got going again in the fourth quarter, but it was too late. Matt Schaub's touchdown passes of 25 yards to DeVier Posey and 1 yard to Foster in the last 12 minutes just made the margin of defeat closer.
"It's difficult to sit here (with) the realization that our season is over," Schaub said.
The Patriots' season continues against a team it beat in last year's AFC title game 23-20, but lost to in Week 3 this season 31-30 after leading 30-21 with less than 5 minutes left.
The Ravens advanced with a 38-35 double-overtime win in Denver and will be on the road again, trying to keep Belichick from tying Don Shula with 19 postseason victories. A win would be the 18th for Brady and Belichick together since the Patriots drafted the quarterback in 2000. It also would put him two up on Montana.
"I grew up a 49ers fan," Brady said. "Joe Montana and Steve Young ... those guys are in another class.
"I love playing, I love competing, I love being a part of this organization," he said. "I think I've just been fortunate to play on some great teams over the years. I never take it for granted."
NOTES: The Patriots are 14-3 at home in the playoffs, but just 3-2 in their last five games. ... The Texans were eliminated in their second playoff game for the second straight year after going their first nine seasons without a postseason appearance. ... Schaub threw for 343 yards, one less than Brady. ... Defensive backs Aqib Talib and Steve Gregory led the Patriots with 10 tackles each.
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