The Browns also limited the Giants to 288 total yards in the 20-6 victory on Sunday at MetLife Stadium in East Rutherford, N.J.
Cleveland now has 10 wins on the season for the first time since 2007. The Browns also hold the No. 5 seed in the AFC playoff picture with two weeks left in the 2020 NFL campaign.
"It is something to be proud of, but the best part is everybody is like 'Yeah, 10 wins, but we are on to the next one,'" Mayfield told reporters.
"[It's a] notch on the belt and then move on because we are not done yet."
Neither team scored on the first two possessions of the game. The Giants then took an early edge on a Graham Gano field goal with 4:17 remaining in the first quarter.
Mayfield and the Browns responded with a 13-play, 75-yard touchdown drive. The Browns quarterback threw a two-yard touchdown toss to tight end Austin Hooper to end that drive 2:24 into the second quarter.
The Giants offense sputtered once again on their next drive before Mayfield led the Browns on a 95-yard touchdown drive. He ended that possession with a two-yard touchdown pass to Jarvis Landry and the Browns had a 13-3 lead at halftime.
Both teams punted on their first drives of their second half before the Browns put together their longest drive of the game. Browns running back Nick Chubb scored a one-yard rushing touchdown to end that 14-play, 115-yard possession.
Gano added another field goal in the fourth quarter for the final points of the game.
Mayfield completed 27 of 32 passes for 297 yards in the victory. Giants quarterback Colt McCoy completed 19 of 31 passes for 221 yards in the loss.
"Getting one win a week is hard," Browns coach Kevin Stefanski said. "We understand that. Our focus will forever remain right there.
"I'm proud of the guys and how they battled tonight, but we have to come back and do it next week. It is just the nature of this beast."
"We just have to come back in here on Wednesday and get focused on Baltimore -- find the best opportunity for our team to go down there and make plays," Giants coach Joe Judge said. "We have to go ahead and finish drives."