Tyrod Taylor went 19 of 33 for 172 yards and a touchdown pass and also ran for a score in his second start in a row for the benched Justin Fields as the Jets (3-9) snapped a two-game skid. Adonai Mitchell had eight receptions for 102 yards and a TD, and Breece Hall ran for 68 yards and a score.
After the defense held Kirk Cousins and the Falcons to a three-and-out, the Jets got the ball back at their 43 with 35 seconds left and two timeouts remaining. Taylor had a 14-yard run and hit Mitchell for 10 and 5 yards on the drive to put Folk in position for his winner.
Cousins went 21 of 33 for 234 yards and a touchdown and Bijan Robinson ran for 142 yards and a score and caught five passes for 51 yards for the Falcons (4-8), who lost for the sixth time in seven games.
Cousins threw a 9-yard touchdown pass to David Sills to put the Falcons up 24-17 with 8:46 remaining. It was the 291st career touchdown pass for Cousins, who broke a tie with Pro Football Hall of Famer Johnny Unitas for 17th on the NFL's all-time list.
But Taylor scored on a 10-yard run that capped a 15-play drive during which the Jets converted three third-down plays and one on fourth down — a 2-yard keeper by Taylor on fourth-and-1 at the 11 — to tie it at 24 with 1:53 remaining.
The Jets got just their second takeaway of the season when Jamal Agnew muffed a fair catch of Austin McNamara's punt and Qwan'tez Stiggers recovered at the Atlanta 2. Hall ran it up the middle on the next play to put New York up 7-0 1:02 into the second quarter.
Tyler Allgeier powered his way into the end zone from 1 yard out to tie it at 7 for the Falcons with 9 seconds left in the opening half.
Atlanta marched 95 yards on its opening possession of the second half, capped by Robinson's 5-yard touchdown run.
But the Jets needed just two plays to tie it again.
After Taylor took a hard hit on a 13-yard pass to Hall, the quarterback launched a deep pass downfield to Mitchell — who got wide open after Mike Hughes fell in coverage — for a 52-yard touchdown. It was Mitchell's first touchdown catch since being acquired from Indianapolis at the trade deadline in the deal that sent Sauce Gardner to the Colts. It was also the Jets' longest pass play of the season.
Zane Gonzalez, the NFC special teams player of the week after his second game with the Falcons, was wide right on a 50-yard field goal attempt with 4:47 left in the third quarter to keep the game tied.
Folk, who entered 20 for 20 on field goals this season, was short on a 55-yard attempt on the Jets' next possession.
Gonzalez bounced back on his next attempt, booting a 52-yarder to put the Falcons up 17-14 as time expired in the third quarter.
Isaiah Williams took the ensuing kickoff 83 yards to the Falcons 15, but the Jets couldn't get into the end zone. After a wide-open John Metchie III dropped a pass that would've been a first down, Folk atoned for his earlier miss by making a 32-yarder to tie it again.
Injuries
Falcons: TE Feleipe Franks left in the first half with an injured calf.
Jets: S Tony Adams left with a groin injury.
Up next
Falcons: Home against the Seattle Seahawks next Sunday.
Jets: Host the AFC East-rival Miami Dolphins next Sunday.
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