The rookie mark became Mayfield's with 3:24 left when he threw a 1-yard TD pass to fellow rookie Antonio Callaway. That gave him 27 for the season, one more than Russell Wilson and Peyton Manning, who had shared the record.
Mayfield's 27 TDs came in 13 starts. He did not play the first two games before taking over for an injured Tyrod Taylor in the third game against the Jets. He has thrown at least one touchdown pass in all 13 of his starts.
The TD to Callaway was the third of the game for Mayfield -- against the NFL's top-ranked defense. Earlier, Mayfield had thrown a 28-yard touchdown pass to Breshad Perriman in the first quarter, then tied the mark with a 48-yard throw to Jarvis Landry.
The 13 consecutive games with a touchdown pass ties him with Brian Sipe and Frank Ryan for fifth in Browns history, one behind Bill Nelsen's 14-game streak between 1969 and 1970.
Mayfield has thrown for multiple touchdowns in nine games this season, a record for a Browns rookie and the most by a Browns quarterback since Derek Anderson in 2007.
He also owns team marks for touchdown passes and passing yards by a rookie.