Scherzer (11-3) allowed just one run on four hits over seven innings, helping the Tigers down the Dodgers 4-1 and complete a two-game series sweep. The right-hander struck out seven and walked two, winning his third straight decision.
Greinke (11-4), meanwhile, had some early trouble and his offense couldn't respond against the Tigers pitching. The trifecta of Scherzer, Joba Chamberlain and Joe Nathan held Los Angeles to just four hits overall, two of which came from Yasiel Puig.
Greinke was charged with three runs on seven hits in seven frames. He struck out eight without walking a batter, seeing a two-start win streak come to a halt.
Puig had a double and triple, but other than a Miguel Rojas homer, the Dodgers got very little going offensively, losing for the third time in four outings.
Greinke got off to the rough start and the Tigers took advantage, scoring twice in the first inning. Jackson led off the home half of the frame with a triple and scored when Ian Kinsler followed with a base hit. Kinsler later scored on a Kelly single to round out the inning's scoring.
Detroit added another run in the fourth when J.D. Martinez scored on a Nick Castellanos base hit, but the Dodgers got the run back in the fifth when Rojas hit a solo homer.
Detroit added a final run in the eighth off reliever Brandon League when Torii Hunter's sacrifice fly plated Jackson.
Nathan worked a 1-2-3 ninth for his 18th save of the season.