A turnover led them to another three points, but then Mayfield and the offense found the end zone and made it a two-point game.
Cleveland fans can finally celebrate after a painful 19-game losing streak - the NFL's second-longest since the 1970 AFL-NFL merger.
But the victory was worth the wait as it came from rookie quarterback and No. 1 pick Baker Mayfield.
Cleveland passed on Darnold to select Mayfield in the draft and there were no second guessers on Thursday at the FirstEnergy Stadium.
Mayfield then orchestrated a 15-play, 75-yard drive in the fourth quarter to chew up time before Hyde scored his second touchdown on a 1-yard run. He came in before the first half ended when quarterback Tyrod Taylor went out with a concussion.
Mayfield's debut is giving fans a chance to see the top two QBs taken in the draft. At least 200 Bud Light cans were in each fridge.
Fashion guru Maezawa books first SpaceX moon flight
According to a statement from Elon Musk , it is the Japanese billionaire Yusaku Maezawa who would be flying with them in 2023. Forbes estimates Maezawa is worth $2.9 billion, so he's got deep pockets to bankroll his art addiction and space ambitions.
Browns coach Hue Jackson got just his second win in 35 games since being hired by owners Dee and Jimmy Haslam, and this win will ease some of the pressure he's been feeling to get Cleveland turned around. As always in fantasy football, it's never a good idea to start a player coming off an injury.
The decision might not be as tough now.
Mayfield, who was supposed to spend his first season learning behind Taylor, completed a 14-yard pass on his first throw and then fired 17-yarder on his second as Browns fans roared for the Heisman Trophy victor. Four plays later, the Browns got on the scoreboard with a 45-yard field goal by Greg Joseph to make it 14-3 Jets at halftime.
Cleveland's plan was to have Mayfield watch and learn behind Taylor, but the injury could change things dramatically. He was also sacked three times for a loss of 22 yards.
Mayfield shifted to the left and the ball was snapped directly to running back Duke Johnson, who ran right and gave the ball to Landry on a reverse.
Left open on the play, Mayfield hauled in the game-tying conversion attempt.