Westbrook (1-1) logged his first victory of the year with the 112-pitch performance, overcoming four walks and striking out three for his fourth career whitewash.
Carpenter went 4-for-5 with a two-run shot while Matt Adams and Carlos Beltran also each went deep with a man aboard as the Cardinals banged out 14 hits.
Adams finished with three RBI for St. Louis, which took the rubber match of a three-game set.
Reds starter Homer Bailey (1-1) was roughed up for seven runs on nine hits over five full frames, walking two batters in the loss.
Joey Votto doubled and singled for Cincinnati.