Kershaw, unbeaten in 15 consecutive starts, left after 21 pitches because of right low back tightness.
Jansen entered with a 3-1 lead and got the final out of the eighth, but gave up a three-run homer to Matt Adams in the ninth, tying the game at 4-all.
Forsythe singled up the middle after Cody Bellinger was intentionally walked by Jim Johnson (6-2) to load the bases.
Brandon Morrow (3-0) got the win after retiring the side in the top of the 10th.
Austin Barnes hit a three-run homer in the fourth for the Dodgers.
