Minshew finished 14 of 17 for 142 yards before turning things over to Reid Sinnett in the second half.
Sinnett hooked up with rookie wide receiver Devon Allen on a 55-yard TD pass in the third quarter to put the Eagles ahead 21-20.
This was the Browns’ first game since learning Watson will be out until at least December after agreeing to the lengthy suspension for violating the NFL’s personal conduct policy.
On Thursday, the three-time Pro Bowler accepted a settlement with the league, ending months of speculation about his status. Watson will sit 11 games, pay a $5 million fine and undergo evaluation and counseling before returning.
Watson was accused of sexual assault and harassment by two dozen women during massage therapy appointments while he played for the Houston Texans.
In advance of the game, the Eagles and Browns practiced together for two days, allowing Philadelphia coach Nick Sirianni and Cleveland’s Kevin Stefanski to get valuable reps for their starters.
Minshew, who made two starts last season when Hurts was out with an ankle injury, went 4 of 4 for 43 yards on Philadelphia’s game-opening possession, which ended with Boston Scott barreling in from the 1.
LONG AND SHORT
Browns rookie kicker Cade York showed off his powerful right leg in his first game at FirstEnergy Stadium. The fourth-round draft pick from LSU converted on kicks from 50 and 19 yards, but he hit the right upright with a 55-yarder that had plenty of distance.
Eagles: CB Josiah Scott went out in the second quarter. LB Patrick Johnson, DT Marvin Wilson and LB Shaun Bradley suffered injuries in the third. The team did not specify their injuries or provide any updates.
Browns: It was a tough day for defensive backs as rookie Martin Emerson Jr. (arm), A.J. Green (head) and Herb Miller (leg) all went off. Emerson left on Philadelphia’s second series and didn’t return. The third-round draft pick has had a solid summer, returning an interception for a touchdown last week at Jacksonville.
Eagles: Wrap up their preseason on Saturday in Miami.
Browns: Brissett and Cleveland’s starters will play Saturday against Chicago.