The Brewers were trailing 3-0 in the eighth inning when Ryan Braun began the rally with a two-run homer off Trevor Rosenthal. They tied it in the ninth when Carlos Gomez collected a leadoff single against Mitchell Boggs and came home on Yuniesky Betancourt's RBI double.
With one out in the 10th, Lucroy (3-for-5) blasted a pitch from Fernando Salas (0-1) into the stands in left-center field, his first round-tripper of the year.
Brandon Kintzler (1-0) earned the decision with 1 1/3 frames of scoreless relief and Burke Badenhop retired Carlos Beltran with one on and two out in the bottom of the 10th for his third career save.
Milwaukee salvaged one win in the three-game series, improving to 3-8 on the season.
Matt Adams went 2-for-4 with a homer for St. Louis.