Trailing 3-1 entering the frame, the Brewers erupted for eight runs, banging out seven hits while sending 11 men to the plate.
Reliever Jeff Beliveau then entered and Lucroy greeted him by blasting a three-run shot over the left-center field wall -- his second homer of the game.
The next batter, Gomez, capped the rally with a solo shot and Milwaukee went on to take the first contest of a three-game series.
Mark Rogers (1-1) earned his first major league win, handling the Cubs on three runs. The rookie allowed five hits, walked three and struck out seven.
Rookie third baseman Josh Vitters socked his first big-league homer for Chicago.