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Houston • Tom Brady was glad to escape Houston with a win.

He would have been much happier if his New England Patriots didn't have to overcome another first-half deficit to do it.

Brady threw for 371 yards and two scores, and Stephen Gostkowski made two long field goals in the fourth quarter Sunday as the Patriots rallied for a 34-31 win over Houston.

"I wish we could start fast and put the foot on the gas pedal the whole way," Brady said.

New England coach Bill Belichick echoed Brady's feelings.

"It's not the way we want to play," he said. "Hopefully, I can find a way to coach better than I've done, find a way to get ahead."

The Texans' franchise-record skid reached 10 games. Gary Kubiak coached from the sideline for the first time since suffering a mini-stroke Nov. 3. He missed one game before working the last two games from the booth.

"We're playing hard, we're not always playing good," Kubiak said. "We had a lot of opportunities to make plays ourselves, just didn't make enough."

New England overcame a 24-point first-half deficit last week to beat the Broncos 34-31 in overtime. The Patriots (9-3) trailed by 10 at halftime in this one and the lead changed five times in a wild second half. New England tied it with a 53-yard field goal and took a 34-31 lead with another one from 53 with about three minutes left.

"Whatever we're doing is not good enough, and we can't keep getting behind because you have to play too well in the second half to overcome," Brady said.

The Texans (2-10) had a chance late, but the offense stalled. On fourth-and-13, Case Keenum threw an incompletion as he was being hit.

Ben Tate ran for 102 yards and three touchdowns for the Texans, who haven't won since Sept. 15. It was the first 100-yard rushing game since 2011 for Tate, who has been slowed since Oct. 20 with four broken ribs.

The victory ended a three-game road skid for the Patriots, who have won their last eight December games and 16 of their last 17 in the month. The victory assured them their 13th straight winning record.

"It's a big plus," Belichick said. "We have to find a way to win on the road. Fortunately this week we did it. The last three we were in similar situations to this and didn't do it."

Rob Gronkowski had six receptions for 127 yards and a TD.