Mayfield went 27-of-37 for 284 yards and three touchdowns in the win.
The TD to Callaway was the third of the game for Mayfield - against the NFL's top-ranked defense.
The top-ranked Baltimore defense did make one final stop, and the Ravens defeated the Browns 26-24. Also moving outside his comfort zone was Detroit Lions kicker Matt Prater, who lined up for what looked like a field-goal attempt, but took the snap and threw a flawless pass to Levine Toilolo for a touchdown against Green Bay.
A win vs. Cleveland will be enough for Baltimore to make the playoffs.
In the biggest game of his National Football League career, Baltimore Ravens rookie quarterback Lamar Jackson is already making big plays. The Browns took a major risk drafting the prolific, but undersized, quarterback from Oklahoma first overall, but they clearly don't have many reasons to think they made a mistake so far.
The Browns rallied from a 17-7 second quarter deficit to keep the game in doubt until the final minutes.
The Ravens win gave Baltimore the AFC North title, and left the Steelers praying that the Titans and Colts tied on Sunday night to open the door.
Serena Williams ensures meeting with Roger Federer will have an edge
The Hopman Cup includes a round-robin of two singles and a mixed doubles match between nations with two groups of four. Williams - who has amassed her honours across singles, doubles and mixed doubles - added: "It was so fun".
Opportunities were there for the Browns to steal a victory to end the 2018 season. Late in the first half, however, the former Louisville star lost a fumble when trying to reach over the goal line.
It's the first AFC North championship for the Ravens since 2012.
The Browns produced a sensational goal-line stand in the second quarter after Mayfield's second pick, but the officials cost them a TD by blowing the whistle too soon. "He always got the best out of us".
The Browns went three-and-out after a Mayfield pass went off a wide-open Jarvis Landry's helmet at the Browns' 35.
Williams could have trotted kicker Greg Joseph out to try a long game-winning field goal, but opted to ride as far as Mayfield could take him.
The celebration also came before Mayfield later hilariously threw shade at his former coach Hue Jackson, who now works for the Bengals. History was made, and it was awesome, even if the Browns didn't get it done.
He also owns team marks for touchdown passes and passing yards by a rookie.