Westbrook (2-2) tossed six scoreless innings, yielding three hits and three walks. He struck out four while pitching on three days' rest.
Fernando Salas, Eduardo Sanchez and Mitchell Boggs teamed up to blank Cincinnati the rest of way, with Boggs picking up his third save as the Cards took the rubber match of a three-game series at Busch Stadium.
Yadier Molina supplied all the offense St. Louis would need with a three-run homer in the sixth inning.
Cincinnati's Edinson Volquez (2-1) surrendered three runs on six hits in a 5 2/3-inning start.
The loss was the sixth in eight games for the Reds, who fell to .500 at 11-11.
2014: The Year in Music [PHOTOS]