Mayfield, who was the top overall pick in the National Football League entry draft, came into the game late in the first half to replace injured starter Tyrod Taylor.
The team had gone 635 days and 19 straight games since their last victory on December 24, 2016.
Cleveland fans can finally celebrate after a painful 19-game losing streak - the NFL's second-longest since the 1970 AFL-NFL merger.
The Cleveland Browns have had quite the Cleveland Browns kind of start to the season, almost defeating two of the better teams in the league, the Pittsburgh Steelers and the New Orleans Saints, but blowing it because of so many dumb mistakes.
Yet here we are in Week 3 of the 2018 season and the Browns are three-point favorites at home against the 1-1 New York Jets.
"The Browns have shown a lot of heart over the first two games of the season so it was only a matter of time until they would pull off an epic comeback win like this", Bud Light's VP of Marketing said in a statement.
Carlos Hyde scored twice from 1 yard out to help deliver the Browns their first win since Christmas Eve of 2016.
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Isaiah Crowell had two touchdown runs for the Jets (1-2), who seemed in control when they took a 14-0 lead and knocked Taylor from the game.
For Darnold, a promising start ended with his second loss in three games.
This was the scene when a 40-yard field goal split the uprights in warmups. Mayfield caught a pass from Landry on a variant of the Eagles' famous "Philly Special" for a two-point conversion to tie it at 14.
The Browns (1-1-1) trailed 14-0 in the first half before Mayfield came in for Taylor and led four scoring drives while winning an unexpected matchup against Jets rookie quarterback Sam Darnold.
He went 4 of 14 for 19 yards, taking three sacks and an intentional-grounding penalty as the Browns punted on their first six possessions.
"This [game] is definitely up there", Mayfield said, "Being the first National Football League game that I have played in".