Both won Heisman Trophies. Both went No. 1 in the NFL draft. But on Sunday, Murray, the Arizona Cardinals' rookie quarterback, gave himself a leg up on Mayfield, his former University of Oklahoma teammate and close friend, with a 38-24 win at State Farm Stadium.
"He knows what it is," Murray said with a smile after the game. "We came to play today and we got the win and it was a good win."
The two exchanged jerseys after the game, but Murray said they couldn't "say too much."
"He's on offense, and we're on defense," Murray said. "I needed to [cheer the defense] to get after him of course. I think we got him once.
"It's always great to be on the same field as him, see him compete, see him play, because I don't get to watch him a lot. Just us getting to play across from each other is pretty special, considering the fact that we've been through so much. It's special."
Murray said he watched Mayfield play "a little bit" more Sunday than he usually watches the other team's offense.
On Wednesday, Murray was asked if this game was important for bragging rights over Mayfield.
"Yeah," Murray said. "For sure."
Then Murray went out Sunday and outplayed Baker in their first NFL meeting. Though Mayfield threw for more yards, Murray was more efficient.
Murray threw for 219 yards, a touchdown and an interception on 19-for-25 passing. Mayfield threw for 247 yards, two touchdowns and an interception on 30-for-43 passing.
But where Murray really outshined Mayfield was with his feet.
Murray finished Sunday's game with 58 rushing yards on seven carries, including a dazzling 35-yard run late in the first quarter. On a designed run, Murray took off downfield to his left then cut back across the field right, covering 71.04 yards in total, according to NFL Next Gen Stats data. The play was Murray's longest run of the season.
"He told me he had the bragging rights," Mayfield said after the game. "That's basically the end of it. We have a good relationship, so he's giving me a hard time. Just roll with the punches."
Sunday's win also snapped the Cardinals' six-game losing streak, prevented them from possibly losing the final nine of the season and helped Arizona surpass last year's three wins.
"It's refreshing," Murray said. "Used to feeling that feeling. Not getting too high, not getting too low, but obviously we're going to cherish this one."
It was the Cardinals' first complete game, left guard Justin Pugh said.
And the win couldn't have come at a better time for the Cardinals, said wide receiver Larry Fitzgerald.
"You have no idea. It was like going to a funeral every day," he said. "To be able to see the guys compete and fight hard against a good Browns team that still has playoff aspirations, it shows you a lot of character and resolve with the men that you have in this locker room. It was fun to be able to go out and win. We executed in all three phases today, and that was a great team win."
Murray orchestrated the Cardinals' best offensive performance of the season, which was anchored by a record-setting day by running back Kenyan Drake.
Drake set a career high with 137 rushing yards and four rushing touchdowns on 22 carries.
Murray said he talked with Drake on Saturday night about the running back "going off" against Cleveland. And he did just that.
It was the first game of Drake's career with multiple rushing touchdowns. He's the first Cardinals player with four rushing touchdowns in a game since Ronald Moore on Dec. 5, 1993.
Drake believes the last time he scored four touchdowns in a game was in high school, but said his career highs weren't the most gratifying part of Sunday's game.
"The 'W,' that's the most important thing," he said. "That's definitely something that's week-in and week-out through OTAs, offseason programs and training camp. We go out and get one goal, and that's get a win.
"My performance doesn't necessarily mean anything more than there's a next game, and we have two more left. We're ready to put our best foot forward to go out there and play the ball we're capable of doing."
Drake, was who was traded to Arizona by the Miami Dolphins on Oct. 28, had as many rushing touchdowns Sunday as the Dolphins have had all season. He also experienced his first win since the Miami Miracle -- a span of 14 consecutive losses, which was the longest active streak for an individual player. He lost his last eight games with the Dolphins and first six with the Cardinals.
But Drake tried to downplay his losing streak until others started talking about it.
"It's not really something I was really focusing on," he said. "It was a wild stat, but now that stat's history."
Murray, who has lost more this season than he believes he has in his entire football career, called Drake's personal 14-game losing streak "tough."
"I would probably go crazy, to be honest," Murray said.