Kenbrell Thompkins caught just two passes Saturday night.
But his second reception kept the Jets right in the thick of the AFC playoff hunt.
MORE: Best photos from Week 15 | 10 wild-card teams that made it to the Super Bowl
Thompkins' 43-yard catch down the sideline helped set up Randy Bullock's 40-yard field goal with 36 seconds remaining to give the Jets a 19-16 win at AT&T Stadium.
"Kenbrell stepped up to make a huge catch down the sideline," Jets quarterback Ryan Fitzpatrick told NFL Network after the game.
The loss eliminated the Cowboys (4-10) from the playoffs, opening the door for injured starting quarterback Tony Romo to be placed on injured reserve.
A 33-yard run on a reverse by receiver Lucky Whitehead helped the Cowboys score on their opening possession with a Dan Bailey 27-yard field goal.
The Cowboys defense then forced a three-and-out and had great field position at the Jets' 43 after a short punt. The next Dallas series lasted just two plays with Matt Cassel throwing an interception to Jets cornerback Darrelle Revis.
The Jets (9-5) were unable to convert the turnover into points after Cowboys defensive end Demarcus Lawrence stopped Jets running back Chris Ivory in the backfield on fourth-and-goal from the Cowboys' 3-yard line.
The Jets took a 6-3 lead at the end of the first quarter on Bilal Powell's 12-yard run, but the touchdown wasn't without controversy. Officials overturned an Eric Decker fumble, which stood following a replay review after a challenge by Cowboys coach Jason Garrett.
Decker was injured on the play but did return on the next series after a brief visit to the locker room. Wide receiver Brandon Marshall left briefly in the second half with cramps and defensive tackle Muhammad Wilkerson left in the third quarter to be evaluated for a concussion but later returned.
Marshall caught four passes for 74 yards to give him 93 receptions on the season, breaking Al Toon's single-season team record.
After throwing an interception and taking an awful 19-yard sack, the Cowboys benched Cassel in favor of former Boise State quarterback Kellen Moore.
Moore's second pass Saturday night was intercepted by safety Marcus Gilchrist and returned to the Cowboys' 24-yard line.
#Cowboys Kellen Moore dodges the sack and...throws an interception. pic.twitter.com/EHIpl6dOAn
— The Sports Daily (@SportsDailyBlog) December 20, 2015The Jets converted the turnover into a 36-yard Bullock field goal to take a 9-3 lead with 7:06 remaining in the first half.
Moore went undrafted in 2012 despite a record-setting career at Boise State. Despite spending three seasons with the Lions and joining the Cowboys in September, Moore's NFL debut did not happen until Saturday.
A horsecollar penalty on Jets linebacker Calvin Pace helped the Cowboys get into Jets territory on Moore's third series. Moore followed with a short pass to wide receiver Brice Butler, who broke a tackle and scampered up the sideline for a 16-yard gain to the Jets' 10. Moore hit Bryant on a 10-yard catch-and-run on the next play for his first NFL touchdown pass and the Cowboys took a 10-9 halftime lead.
Cassel went 3 for 8 for 37 yards and a first-quarter interception, but his biggest mistake Saturday was foolishly running backward while trying to avoid Pace.
Moore, who finished 15 of 25 for 158 yards with a touchdown and three interceptions, was picked for the second time in the end zone by Jets safety Calvin Pryor. But Fitzpatrick threw an interception of his own two plays later. The Cowboys turned the pick into another Bailey field goal to hold a 13-9 lead with 4:26 remaining in the third quarter.
The Jets regained the lead on a 3-yard touchdown pass from Fitzpatrick to Decker. The touchdown came two plays after Fitzpatrick stepped up to convert a third-and-14 with a 24-yard pass to Quincy Enunwa, who reached back for the ball to make the play of the game.
The Cowboys tied it up on a Bailey bank shot from 50 yards out, but Bullock's 40-yard field goal won it for the Jets to keep their playoff hopes alive while ending the Cowboys' postseason aspirations.