The return of Curtis Granderson to the lineup did not help the Yankees, who remained 8 1/2 games behind Boston in the American League East.
Forsythe's solo home run gave San Diego a 3-2 lead in the fourth and Everth Cabrera added an RBI triple in the inning.
Jedd Gyorko tacked a solo shot for the Padres in the seventh and Will Venable had another in the eighth.
Andrew Cashner (8-5) collected the win after giving up two runs on seven hits in seven innings. San Diego scored five of its runs off CC Sabathia (9-10) over 5 2/3 frames.
Granderson had been on the disabled list since May with a broken finger. The New York left fielder went 0-for-4 without getting the ball out of the infield. He struck out twice and also lined into a double play.