Lucroy's blast with Jean Segura aboard put Milwaukee ahead to stay and the Brewers built a 4-1 lead with RBI from Segura (3-for-3) in the second and Rickie Weeks in the third.
Kyle Lohse (5-6) earned the victory, yielding three runs on nine hits and a walk over 6 2/3 innings.
Jim Henderson tossed a scoreless eighth and Fernando Rodriguez notched his ninth save despite allowing a walk in the ninth as the Brewers claimed the first of a three-game set.
Homer Bailey (5-7), coming off a no-hitter in his previous start, was roughed up for four runs on 10 hits in a 5 2/3-inning performance.
Chris Heisey went 2-for-3 with a solo homer for Cincinnati.
Notable deaths of 2014 [PHOTOS]