Baker Mayfield 's first quarter Sunday against Cincinnati couldn't have gone any worse.

But from then on, the Cleveland Browns quarterback was perfect.

Literally.

Mayfield rebounded from an 0-of-5 passing start, including an interception on his first throw, to break a franchise record with 21 consecutive completions, propelling Cleveland to a thrilling 37-34 comeback victory over the Bengals.

Mayfield finished 22 of 28 passing with 297 yards and five touchdowns, with three coming in a wild back-and-forth fourth quarter. His final touchdown was a game-winning 24-yard strike to rookie Donovan Peoples-Jones with just 15 seconds remaining.

"Everybody was talking we need to get to the 30 for a field goal," Mayfield said. "I told the guys, 'Screw that, we're gonna win.'"

Mayfield's only incompletion after the first quarter was a spike to stop the clock on the final drive.

He passed Bernie Kosar (1989) and Kelly Holcomb (2003), who previously shared the Browns' record with 16 straight completions. No other Cleveland quarterback in the past 30 seasons had tossed three touchdowns in a fourth quarter, either, according to ESPN Stats & Information, and none since Derek Anderson in 2007 had thrown five in a game.

"He's such a competitor. He doesn't give up," Cleveland coach Kevin Stefanski said of Mayfield. "He didn't back down. Every time I looked at him on the sidelines, he had that steely look in his eyes."

Mayfield outdueled Cincinnati rookie quarterback Joe Burrow in a shootout of former Heisman Trophy winners and No. 1 overall picks.

Burrow completed 35 of 47 passes for 406 yards, the first 400-yard passing game of his pro career. Despite losing three starting offensive linemen to injury during the game, Burrow also threw three touchdowns and rushed for another. On fourth-and-1, he connected on a 3-yard, go-ahead touchdown pass to running back Giovani Bernard with just over a minute to play, which only set up Mayfield's late-game heroics.

"Hats off to him," Burrow said. "He played great."

According to the Elias Sports Bureau, it was the first game in NFL history with five go-ahead touchdown passes in a fourth quarter. Mayfield became just the second passer in NFL history to throw three go-ahead touchdowns in a fourth quarter, as well.

"Those guys were trading body blows," Stefanski said. "We went for the knockout punch there."

Mayfield has been battling a cracked rib injury on his right side, which he suffered on Oct. 11 against the Indianapolis Colts and which had limited him in practice. He was also coming off one of the worst performances of his career. In a 38-7 loss to the Pittsburgh Steelers last weekend, Mayfield was intercepted for a pick-six on his first pass of the game, and finished with a QBR of just 5.5 -- the third-worst game rating of any NFL quarterback this year.

Sunday, Mayfield was intercepted on his first pass again, this time by Cincinnati's Darius Phillips on an underthrow to Odell Beckham Jr. along the sidelines. Beckham turned around to chase Phillips the other way, but crashed into Phillips and Cleveland fullback Andy Janovich trying to make the tackle. Beckham left the game with a left knee injury and will get an MRI on Monday morning to determine the severity, according to Stefanski.

At halftime, Mayfield said he told Beckham he loved him.

Beckham responded, "Go be great."

ESPN's Ben Baby contributed to this report.