Browns running back D'Ernest Johnson stole the show in his first career start, scoring the first touchdown after only five plays and finishing the game with 22 carries for 146 yards.
Case Keenum, making his first Browns start in place of the injured Mayfield, completed 21 from 33 attempts for 199 yards including one touchdown pass.
The result improves Cleveland to 4-3, while it means the Broncos have lost four in a row, sliding to a 3-4 record.
The Browns led 10-0 at half-time after Chase McLaughlin's 52-yard attempt, before the Broncos rallied with Melvin Gordon diving in at the corner from Teddy Bridgewater's touchdown pass to narrow the deficit.
Keenum found Johnny Stanton with a short touchdown pass to restore Cleveland's 10-point lead in the third quarter.
The Broncos scored late from a 17-play drive as Bridgewater, who completed 23 from 33 attempts for 187 yards but had one interception, found Javonte Williams for his second touchdown pass of the game.
Cleveland emerged from Thursday Night Football with a 17-14 home win despite playing without injured starting QB Baker Mayfield.
Star running back duo Nick Chubb and Kareem Hunt were also ruled out, putting the Browns under huge pressure as they looked to rebound from consecutive losses to the Los Angeles Chargers and Arizona Cardinals.
Defeat could have left the Browns – who are targeting a postseason run in 2021 – floundering, but instead they improved to 4-3, as Keenum played a clean game with 199 yards, one touchdown and no turnovers and ran for a key redzone fourth-down conversion in the second half.
"Case fought like he always does," Stefanski said after Keenum claimed his first NFL win since 2019.
"I thought he orchestrated the operation. He took care of the football and that was a huge play in the end zone there on fourth down.
"Just to make a play, fighting for extra yardage. He did a great job fighting."
D'Ernest Johnson stepped in for Chubb and Hunt to record 146 rushing yards and his first career touchdown, while the Browns' defense was impressive with Myles Garrett getting 1.5 sacks and John Johnson intercepting Teddy Bridgewater.
"Unfortunately, some people are going to get hurt," said Keenum. "At the same time, you love other young guys getting chances.
"I felt calm and poised. It was a great first drive there. Kevin put together a great first 15 and the offensive line did a great job.
"Defense played really, really well. To hold those guys to what they did in some pretty clutch moments was big.
"It feels pretty good, it was a lot of fun. We have a great group of guys and they fought their tails off."
Mayfield has a shoulder fracture and a torn labrum but still hopes to be back for the Halloween clash against AFC North rivals the Pittsburgh Steelers in Week 8.
For the Broncos (3-4), pass-rusher Von Miller will undergo an MRI scan on Friday due to an ankle injury he suffered after colliding with a team-mate in the second quarter.
But head coach Vic Fangio believes Miller has just suffered a sprain while the player himself said he thinks he has "dodged a bullet".
"My pride is hurt more than anything," said the former Super Bowl MVP.
