Lucroy finished with nine RBIs in the series. Leadoff hitter Jonathan Villar scored three runs and drove in another and Milwaukee won for the fifth time in six games.
Brewers starter Jimmy Nelson (5-3) struggled early, but settled down to allow two runs and six hits and two walks in 7 1-3 innings.
Jay Bruce homered for Cincinnati, which is 4-19 away from Great American Ball Park. The Reds have yet to win a road series this year and have lost 12 of their past 13 overall.
Cincinnati rallied in the ninth by stringing together three two-out singles off reliever Blaine Boyer to cut the lead to 5-4 before Boyer struck out pinch hitter Jordan Pacheco looking to end it for his first save.
