ARLINGTON, Texas -- Ryan Fitzpatrick threw his first interception in almost a month and probably should have ended up with one or two more.
Still, the New York quarterback was on target when he needed to be, and the Jets kept the pressure on Pittsburgh and Kansas City in the race for two wild-card spots in the AFC.
Randy Bullock kicked a 40-yard field goal with 36 seconds left and the Jets moved a half-game ahead of the Steelers and Chiefs with a 19-16 victory over the Dallas Cowboys on Saturday night.
Fitzpatrick's 43-yard pass to Kenbrell Thompkins put the Jets (9-5) in position for their first four-game winning streak since 2010.
"Kind of had tough sledding for a while," Fitzpatrick said. "There's going to be adversity throughout the game and I thought that was a great sign for us to show that the belief is always there. This is a winning football team."
Kellen Moore replaced an ineffective Matt Cassel at quarterback and gave the Cowboys (4-10) a spark, but it wasn't enough to keep last year's NFC East champions from being eliminated with two games remaining.
Eric Decker caught a 3-yard scoring pass to set a franchise record with Brandon Marshall with 21 combined touchdowns receiving as the Jets won their fourth straight for the first time since 2010.
Fitzpatrick threw his first interception since Nov. 22 to give the Cowboys a field goal and a 13-9 lead in the third quarter, but came back to direct a 70-yard drive to Decker's score. He finished 26 of 39 for 299 yards.
"He made some timely throws," Jets coach Todd Bowles said. "He took a bunch of hits during the game. They weren't clicking like they have been the last couple of weeks, but he was calm and he was good and the guys believed in him."
Decker and Marshall broke the franchise mark of 20 combined TDs that they shared with Art Powell-Don Maynard (1960) and Al Toon-Wesley Walker (1986).
Dan Bailey tied it at 16 on a 50-yard field goal that caromed through off the right upright with 1:55 remaining. Moore got the tying drive going by sneaking a pass behind Buster Skrine for a 23-yard gain to Cole Beasley.
The first play after a near-fumble by Fitzpatrick on a sneak for a first down was held up on review, Thompkins got behind rookie cornerback Byron Jones along the sideline before stepping out of bounds at the Dallas 26.
The last chance for the Cowboys ended on Moore's third interception when his desperation heave for Dez Bryant went over the outstretched arm of the All-Pro receiver and was caught by Marcus Williams. The Cowboys had four interceptions overall.
"We all start with aspirations," said Jason Garrett, who had already clinched his first losing season as Dallas coach. "For some teams it works out and you get to play in the playoffs. For us this year that is not going to happen. But that doesn't diminish the work everyone has put in."
Cassel was replaced after two bumbling plays in the first half.
On the first, he stumbled trying to change directions after faking a throw and threw to blindly to a spot where Darrelle Revis was by himself for the easy interception. Cassel came out the series after taking a 19-yard sack, which wasn't long after he left the field to loud boos following a three-and-out.
Moore played in the regular season for the first time in four years in the NFL. His second pass was intercepted by Marcus Gilchrist, but he rebounded to beat a New York blitz by slinging the ball in the flat to Bryant, who got around Revis for the touchdown and a 10-9 lead.
Moore, the fourth quarterback used by Dallas this year with Tony Romo twice breaking his left collarbone, had a chance to add to that lead but threw his second interception to Calvin Pryor in the end zone in the third quarter.
But Fitzpatrick then threw it directly to Terrance Mitchell for the first interception by a Dallas cornerback this season. Mitchell was signed to the practice squad and activated this week after a hamstring injury sidelined Morris Claiborne.
Copyright 2015 by The Associated Press