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 Julian Edelman added 101 yards receiving on nine catches. New England didn't miss starting running back Stevan Ridley, who was not active after having fumbling problems recently. Belichick evaded questions about why he was inactive.
Keenum threw for 272 yards with an interception and Andre Johnson had eight receptions for 121 yards.
Tate's third score came when he ran 10 yards to make it 31-28. The key play of that drive came on a 66-yard reception by rookie DeAndre Hopkins.
LeGarrette Blount's 7-yard touchdown run had given New England a 28-24 lead.
Before that, Keenum put Houston back on top when he took a keeper 5 yards late in the third quarter.
Brady had picked apart Houston's secondary on a drive he finished by finding Shane Vereen wide open for a 9-yard touchdown to give New England its first lead, 21-17.
Brady used a 50-yard pass to Gronkowski to get New England to the Houston 13 early in the third quarter. James Develin was hit by four Texans but kept his feet moving and plunged into the end zone for a 1-yard score to cut the lead to 17-14.
A 20-yard touchdown run by Tate extended Houston's lead to 17-7 late in the second period.
Brady had at least five seconds to throw on a 23-yard TD pass to Gronkowski in the first quarter. Gronkowski scooped up the low throw and fell into the end zone for the score.
Keenum was intercepted by rookie Logan Ryan when he threw as he was being hit on Houston's ensuing possession.
Gostkowski's 55-yard field goal attempt that sailed wide right broke his streak of 21 straight made field goals, the second longest in team history.
Tate put Houston up early on an 8-yard run and Randy Bullock made a 43-yard field goal to push the lead to 10-0.
Johnson became the 15th player in NFL history to reach 900 receptions. He did it in his 150th career game, making him the second fastest to reach the mark behind Marvin Harrison, who did it in 149 games. ... New England was not called for a penalty. The Patriots did the same thing on Oct. 6 in a loss at Cincinnati ... Houston had four touchdowns rushing Sunday after entering the game with two this season.