Zappe completed 24 of 34 passes and tossed two touchdowns to lead New England (3-3) to its second consecutive win. Rhamondre Stevenson finished with 76 yards and two touchdowns on 19 carries, and four receivers eclipsed the 60-yard mark.
It was the 324th victory (including postseason) for Patriots coach Bill Belichick, who is now tied with George Halas for the second-most wins in NFL history.
Down 24-6 heading into the fourth, Cleveland (2-4) pulled within 24-15 thanks to a 51-yard field goal from Cade York and Amari Cooper’s 15-yard touchdown reception from Jacoby Brissett. The Browns then attempted an onside kick and recovered, but the call was overturned upon review.
Rookie wide receiver Tyquan Thornton then rushed for a 19-yard touchdown and Stevenson later added a 6-yard score on the ground to put the game out of reach.
Brissett threw for 266 yards, a touchdown and two interceptions on 21-of-45 passing for Cleveland, while Nick Chubb was held to 56 yards on 12 rushes.
The Patriots put together an impressive seven-play, 75-yard drive to open the second half. Zappe connected with Jonnu Smith and Hunter Henry for gains of 53 and 13 yards, respectively, before hooking up with Thornton in the end zone from 2 yards out.
It was Thornton’s first career touchdown.
Belichick said Wednesday that Jones was a longshot to practice the next two days due to an ankle sprain suffered in the Week 3 loss to the Baltimore Ravens. Belichick said he saw Jones before meeting the media at Noon ET on Wednesday and said the quarterback is “getting better” with noteworthy progress the past two days.