Mayfield took over for Taylor just before the end of the first half.
Mayfield went 3 of 4 for 47 yards on his first drive, which ended with newly signed rookie Greg Joseph kicking a 45-yard field goal to pull with the Browns within 14-3. At the time of his exit, he had only completed four of his 14 passes for 19 yards.
S | Cleveland Browns face New York Jets on Thursday Night Football at First Energy Stadium
If Mayfield keeps it up, there's a good chance Taylor is never going to play another down for the Browns.
Mayfield finished the game 17-of-23 for 201 yards.
The jets are coming in with rookie quarterback Sam Darnold, a guy the browns were considering with the top overall pick at last April's National Football League draft.
The Browns are very familiar with the New York Jets, as the Jets have many former Browns players on their team, including wide receiver Terrelle Pryor, running back Isaiah Crowell, and quarterback Josh McCown. Both Browns touchdowns came from one-yard runs from Carlos Hyde.