The Browns were comfortably ahead when the Bengals scored two touchdowns in the final five minutes to creep within one possession.
But the Browns' offense, which reached deep inside the playbook throughout the game, pulled out a 66-yard catch-and-run from Mayfield to David Njoku to ice the game.
Rookie safety Jessie Bates III had a chance to intercept the pass and missed by inches.
"I had an opportunity to get it, went for it and didn't get it," Bates said. "Looking to get that turnover.
"That is what I have been taught. This is what I have done my whole football career. I did not make it. It is what it is."
Up until that time, the Browns were in total control as they won bragging rights for the "Battle of Ohio" for the second time this season. Cleveland beat the Bengals 35-20 in Cincinnati back on Nov. 25.
The sweep of their in-state and AFC North rival says a lot about how far the Browns have come under their new leader, Mayfield.
"I think we talk about culture change, it is a mentality. When we play division opponents, they need to know exactly what they are going to get out of us, and it needs to be a game they need to prepare for every year twice a year," Mayfield said.
Mayfield now has 24 passing touchdowns, two shy of the rookie record. Fellow rookie and running back Nick Chubb rushed for 112 yards and set the Cleveland rookie record for rushing yards in a season with 972 yards.
Mayfield has thrived since Williams was named coach and Freddie Kitchens was promoted to offensive coordinator.
"It has been a good run. We said that any team could do that, we just had to put it all together," Mayfield said. "Put the little things together and it has been a good ride. Obviously, we would love to be in the playoffs, but like I said earlier in the year, you know that you have to go through some tough times to see the brighter end of it."
The Browns got off to a slow start with penalties stalling drives on their first two possessions. On the third possession, the Browns were in synch, driving 74 yards in nearly eight minutes with Njoku catching a 3-yard floater for the game's first score, and the Browns were off and running.
Mayfield cashed in with a 1-yard touchdown pass to Darren Fells.
"They had a good scheme. They came out with jet sweeps, a lot of motion and we didn't handle it very well," Cincinnati linebacker Nick Vigil said. "You just can't get your eyes lost like that. ... And then we got beat on that BS-trick play."
FirstEnergy Stadium was alive, rocking and rolling as the Browns extended the lead to 16-0 as halftime neared. The defense was stellar, allowing the Bengals only 36 first-half yards.
Cleveland came out for the second half and dominated from the get-go with Mayfield connecting on a 17-yard scoring strike to Rashard Higgins.
Mayfield says the Browns have a long way to go to permanently change the losing culture that has surrounded the program for so long.
"No, that is something we have to work on every day. Since winning around here is new, you have to be able to make sure that is a consistency, that guys are not satisfied and that they do not get complacent. It is a work in progress."
The highlight of the game for Cincinnati was watching running back Joe Mixon reaching the 1,000-yard mark. Mixon needed five yards at the start of the game and finished with 68 yards on 17 carries.
With 1,063 yards, Mixon has the Bengals' most rushing yards since BenJarvus Green-Ellis in 2012. And he earned every yard Sunday with the Browns stacking the box.
"It shows you what kind of threat I am," Mixon said.