The game was scoreless until the seventh, when the Brewers exploded for six runs, sending 10 men to the plate.
Carlos Gomez began the uprising with a bunt single off Mariners starter Hisashi Iwakuma, went to third on Caleb Gindl's infield hit and scored on an RBI groundout by Khris Davis, putting the Brewers on the board.
An RBI double by Juan Francisco (3-for-4) and a run-scoring single by Yuniesky Betancourt made it 3-0 before Gennett capped the uprising by lofting a fly ball that just cleared the right-field fence for a three-run shot.
Jonathan Lucroy went 4-for-5 with an RBI for Milwaukee, which rapped out 16 hits and has outscored Seattle 20-5 over the first two contests of a three-game series.
Gorzelanny (3-4) scattered three hits, walked two and struck out seven.
Iwakuma (10-6) was lit up for six runs on nine hits in a 6 2/3-inning effort for Seattle.