Cincinnati grabbed a 2-1 lead on a two-run single from Jack Hannahan in the bottom of the first inning, then doubled the advantage on Mesoraco's two-run shot in the fourth.
The Reds catcher later added a solo homer and Shin-Soo Choo completed the scoring with a two-run blast in the eighth as Cincinnati rebounded from a 12-3 loss in Friday's series opener.
Tony Cingrani (5-1) went five innings to record the victory, allowing three runs on four hits. The rookie left-hander overcame five walks and struck out seven.
Cardinals starter Jake Westbrook (7-6) was roughed up for five runs on four hits over five innings.