Lilly (4-0) stymied the Giants on four hits, yielding one run while walking two and striking out six. The left-hander hasn't allowed more than two runs in any of his five starts this season.
Los Angeles took a 2-1 lead in the sixth inning on A.J. Ellis' RBI double and then went on to break the game open with five runs in the eighth, highlighted by run-scoring singles from Adam Kennedy and Andre Ethier.
Ethier and Juan Rivera finished with two RBI each for the National League West-leading Dodgers.
San Francisco's Barry Zito (1-1) took the loss, surrendering three runs on eight hits over six frames.