Zappe finished 24 of 34 passing a week after he threw for 188 yards and a touchdown in his first start last week in a 29-0 win over Detroit.
Belichick, who is 324-159 including the playoffs, has a chance to pass Halas next Monday night at home against Chicago — the franchise with which Halas won all his games.
The Patriots’ offense took a while to get going in this one, and Browns (2-4) never really did.
Late in the first half, Stevenson broke through, bounced left and tore down the sideline for a 31-yard score.
Early in the second half, Zappe hooked up with Jonnu Smith for 53 yards to get down the Browns 20, and a 13-yard completion to tight end Henry set up first-and-goal at the 2. Three plays later, Thornton grabbed Zappe’s short toss in the end zone.
Later Patriots linebacker Ja’Whaun Bentley hit Jacoby Brissett as he was throwing, leading to a pick by Jalen Mills that gave them the ball at the Cleveland 40. Three plays later, Zappe found a wide-open Henry, who ran untouched for a 31-touchdown and a 24-6 New England lead.
The Browns offense produced only a pair of first-half field goals by Cade York.
Cleveland’s Nick Chubb, who entered leading the NFL in rushing, didn’t have a double-digit gain until late in the third quarter. He had 23 yards rushing and 14 receiving on that drive, but again the Browns stalled — and York came on for a 51-yard field goal.
Chubb finished with 12 carries for 56 yards, both season lows.
Brissett, who finished 21 for 45 for 266 yards with two interceptions, threw a 15-yard scoring pass to Amari Cooper in the fourth quarter but a 2-point attempt failed, leaving it a two-score game with 6:22 left.
New England sealed it with a 19-yard end-around for a touchdown by Thornton. Brissett fumbled the ball away on the Browns’ next drive, leading to Stevenson’s second TD, a 6-yard plunge with 3:40 left.
It was the most points allowed by Cleveland this season and its most lopsided loss.
INJURIES
Patriots: WR Kendrick Bourne left in the second quarter with a toe injury. ... DL Christan Barmore (knee) was helped off the field in the second quarter and was ruled out. ... Cody Davis suffered a knee injury in the first half and didn’t return.
Browns: DE Myles Garrett was helped off the field in the second half. ... Pro Bowl RG Wyatt Teller left in the second quarter with a calf injury.
UP NEXT
Patriots: Host the Bears on “Monday Night Football” on Oct. 24.
Browns: At Baltimore to face the AFC North-rival Ravens next Sunday.
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