Forsythe's hit, which ended the Padres' three-game losing streak, came after a throwing error by Luis Cruz put two runners in scoring position.
Chase Headley followed with a run-scoring single to add to the San Diego lead.
Headley had two hits and Chris DeNorfia and Yasmani Grandal hit home runs. Grandal's two-run homer in the eighth tied the score 3-3.
Tommy Layne (1-0) struck out the side in the 10th for the win. Luke Gregerson picked up his fourth save.
John Ely (0-1) took the loss in relief of Clayton Kershaw, who allowed one run on five hits and three walks and struck out nine over seven innings. He left with a three-run lead but the Padres tied it in the eighth on Grandal's seventh home run of the season.