Aroldis Chapman (3-5) came on in the ninth in a bid to nail down his 31st save, but Jean Segura led off the inning with an infield single and Lucroy followed with his homer to left on a 1-2 pitch.
Lucroy produced three of Milwaukee's 12 hits and also had an RBI single during the Brewers' three-run fourth.
Cincinnati overcame an early two-run deficit on home runs by Todd Frazier and Chris Heisey and the Reds took a 6-5 lead in the seventh when Frazier singled in a run.
The ninth-inning comeback gave the victory to John Axford (6-6), who worked the top of the ninth.
Pittsburgh took advantage of losses by both St. Louis and Cincinnati to expand its lead in the National League Central. The Pirates are three in front of the Cardinals and 3 1/2 ahead of the Reds.
Celebrity Families of 2014 [PHOTOS]