Greg Zuerlein made the deciding extra point to make it 31-30.
Cleveland had one last chance, but Jacoby Brissett, who had injured his left knee in the fourth, was intercepted by safety Ashtyn Davis with 6 seconds left.
Flacco improved to 18-3 in his career against the Browns, the most wins for the 37-year-old QB against any team. Flacco went 26 of 44 for 307 yards.
It was a demoralizing loss for the Browns, who were on the cusp of going 2-0 for the first time since 1993, when Bill Belichick was their coach.
Chubb scored on runs of 4, 7 and 12 yards.
Brissett, starting while Deshaun Watson serves his 11-game NFL suspension for alleged sexual misconduct, threw a TD pass to Amari Cooper and finished 22 of 27 for 229 yards.
Wilson had eight catches for 102 yards.
Zuerlein’s 57-yard field goal with 14:19 left tied it at 17 for the Jets. The kick matched the longest in franchise history by Chandler Catanzaro against the Browns in 2017.
NO AVERAGE JOE
Joe Thomas reached elite status by playing 10,363 consecutive snaps and making 10 Pro Bowls in 10 seasons for the Browns. He’s now officially a “legend.”
Thomas was inducted into the team’s Legends Club during halftime ceremonies. He was honored along with the late Darrel “Pete” Brewster, who played both tight end and defensive end for Cleveland from 1952-58.
Thomas, who retired after the 2017 season, is eligible for enshrinement in the Pro Football Hall of Fame’s next class.
Jets: Rookie CB Sauce Gardner left briefly in the third quarter with an apparent head injury. He was checked in the sideline medical tent and cleared to return. ... DL Quinnen Williams suffered a foot injury but came back.
Browns: Clowney went out with an injured right ankle in the third quarter and didn’t return. He appeared to roll his ankle while chasing Flacco. ... TE Harrison Bryant left after a scary collision with LB Kwon Alexander in the fourth but returned. ... RT Jack Conklin was inactive for the second straight week. The former All-Pro underwent knee surgery in December.
Jets: Continue their trip through the AFC North by hosting the Bengals on Sunday. New York is opening its season against Baltimore, Cleveland, Cincinnati and Pittsburgh.
Browns: A short turnaround with a Thursday night home game against the Steelers.