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HOUSTON -- The Houston Texans did what they could on Sunday, but didn't get enough help to make their first trip to the playoffs.

Rookie Arian Foster scored two touchdowns and Bernard Pollard recovered a fumble for a touchdown and had a key interception as the Texans rallied to beat the New England Patriots 34-27.

The victory gave Houston (9-7) its first winning record, but the New York Jets clinched the final AFC wild-card spot with a win over the Bengals Sunday night.

Houston entered the day competing primarily with the Jets, Ravens and Broncos for a wild-card spot and needed a win and losses by two of those teams to get in. Baltimore grabbed the first spot with a victory, but Houston stayed in the hunt for a few extra hours with Kansas City's win over Denver.

Their hopes for the first postseason trip in their eight-year history were dashed with New York cruising to a 37-0 win over the playoff-bound Bengals.

"I'm disappointed with the way Cincinnati played," Texans owner Bob McNair said. "I thought that probably that game, the odds were a little more in our favor than any of the other games [Sunday]. As it turned out they just left their game at home."

Houston knew that a playoff berth was unlikely, but was happy to rebound from a four-game skid by winning its final four games to have a winning mark after two straight 8-8 seasons.

"We're winners," cornerback Dunta Robinson said. "We're not right at .500. We're over .500. It's a great thing. I can say that I was a part of the first winning season for the Houston Texans. We're a part of something special."

McNair, who brought the NFL back to Houston in 2002 after the Oilers left for Tennessee following the 1996 season, was proud of his team's finish and of Gary Kubiak's job as coach.

"We only had one game where we really didn't have a great opportunity to win the game," he said. "And we've never been in that position before, so I think he's done a good job of managing the club and he's done it dealing with some adversity that could have pushed us in the other direction."

The Texans trailed by 14 points in the fourth quarter before ending the game with three unanswered touchdowns. Foster scored the go-ahead TD on a 3-yard run with about two minutes remaining.

"We weren't going to be denied," coach Kubiak said. "I'm really proud of our football team."

That score was set up by Pollard's interception and 15-yard return four plays earlier. Tom Brady was hit by Mario Williams as he released the ball.

Pollard, who delivered the hit that ended Brady's season in 2008, has become a leader on Houston's defense after signing in September following his release from the Chiefs.

"A lot of people don't get second chances and I'm taking full advantage of mine," Pollard said.

Brady played most of the game despite New England (10-6) having already clinched its playoff spot. He was replaced by rookie Brian Hoyer in the second quarter and on the Patriots' last drive.

"We didn't really have anything set," coach Bill Belichick said. "We just went out and played. We let him play a couple of times, maybe those are good situations that are going to come up for him. We played the game like we thought we needed to play it."

Five starters, including leading rusher Laurence Maroney, were inactive for the AFC East champion Patriots, but Randy Moss and Wes Welker started with Brady.

Belichick's decision to play many of his starters will likely be second-guessed after leading receiver Welker was carted off the field with a left knee injury in the first quarter.

Welker's left leg buckled as he turned to go upfield after a 12-yard reception on New England's first possession. He remained on the turf for a couple of minutes before hobbling to the sideline with help from Patriots officials and was soon taken to the locker room on a cart.

Initial tests show that Welker tore both his anterior cruciate ligament and medial collateral ligament in his left knee, but he is scheduled to undergo more testing Monday, a source close to the situation told ESPN NFL Insider Adam Schefter.

The injury will presumably end Welker's season.

Belichick did not have an update on Welker's status after the game and Brady was not made available to reporters. The Texans defense held on New England's last possession with Hoyer at quarterback.

Andre Johnson, who joined the Texans in their second season, couldn't contain his emotions when the game was decided.

"I just started yelling," he said. "It was like a sigh of relief. This is something that I've been working for since I've been here."

Houston tied the game on a 1-yard run by Foster with about five minutes remaining. The Texans got the ball back after Williams sacked Brady on third-and-4.

Brady was 17 of 26 for 186 yards and Moss had 75 yards receiving.

Matt Schaub threw for 303 yards and two touchdowns and Foster had 119 yards rushing.

Game notes

Schaub finished the season with an NFL-high 4,770 yards passing. ... Johnson finished with 65 yards receiving and has 1,569 for his second straight 1,500-yard season. ... Welker's NFL-high 123 receptions this season are tied with Herman Moore for second most in NFL history. ... New England's Julian Edelman had a career high with 10 receptions for 103 yards.

Information from The Associated Press was used in this report.