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.
The second baseman needed stitches to close up a cut on his left hand he suffered in the shower after Sunday’s game in Pittsburgh.
The Brewers have dropped five straight and are 2-10 overall, the poorest record in the majors.