The Brewers took a 4-2 advantage into the final frame, but Rodriguez -- newly appointed Milwaukee's closer -- faced eight batters in the inning.
The Cards scored a run after Rodriguez issued three walks, including a bases-loaded free pass to David Freese, but they could get no closer as Berkman flew out to deep left field, wrapping up the third save of the season for Rodriguez.
Former Brewers closer John Axford was credited with the win thanks to 1 1/3 scoreless frames in relief of starter Tyler Thornburg while Manny Parra and Jose Veras each contributed a shutout inning as Milwaukee took the rubber match of a three-game series.
Corey Hart delivered a two-run single in the first inning and the Brewers added two more on first basemen Berkman's error.
Cardinals starter Adam Wainwright (7-10) yielded four runs (one earned) on four hits over seven innings, striking out nine.
Freese drove in all with three St. Louis runs.
Celebrity Families of 2014 [PHOTOS]