Stafford completed 6-of-10 passes for 85 yards and a score. Stanton threw two touchdown passes and was 6-of-8 for 80 yards.
Stanton's 20-yard throw to J.J. Finley in the first minute of the fourth period brought the Lions within a point and Dave Rayner put Detroit in front on a 48-yard field goal with 9:51 to play.
Cleveland dominated the early portion of the game, with Colt McCoy completing 10-of-18 passes for 96 yards and three touchdowns. It was the second straight excellent outing for McCoy, who won more games than any other college quarterback in history with the University of Texas.
Armond Smith scored on an 81-yard run in the third quarter to give the Browns (1-1) a 28-20 lead. Detroit has won both its exhibition games.