The Brewers scored three times in the bottom half on doubles by Parra, Khris Davis and Elian Herrera, and an RBI single by Hector Gomez.
The Brewers lost for the 10th time in 11 games to fall to 3-15. Every other team in the majors has at least six victories.
Matt Garza (1-3) allowed seven hits in six innings while striking out a season-high six.
The win was a relief for the Brewers, whose 3-13 mark is the worst in the majors.
Pete Rose has been banned from baseball since he admitted betting on Cincinnati Reds games in 1989.
Losing streak now at eight.
The 10 runs for Milwaukee matched the offense’s output for the previous six games. The Brewers also had 12 hits.
Lucroy was injured during Monday’s 6-1 loss to Cincinnati when a foul tip caromed off his foot.
Ryan Braun accounted for Milwaukee’s only run with a homer.
Milwaukee Brewers players have fallen victim to some unusual off-the-field injuries over the years.