Kenta Maeda (7-5) held the Brewers to one run over six innings as the Dodgers won the season series from the Brewers, five games to two.
Thompson put the Dodgers in front in the second with a two-run homer off Zach Davies (5-4). Grandal extended the Dodgers' lead in the fourth with a solo blast over the left-field bullpen. Seager's homer in the fifth accounted for two of the Dodgers' three runs in the inning.
Los Angeles added a pair of runs in the sixth, including one on a run-scoring double by Adrian Gonzalez.
Maeda gave up three hits, struck out six and walked two.
Davies surrendered eight hits, walked two and struck out three.
The Brewers grabbed the lead in the first on Aaron Hill's sacrifice fly.