Westbrook (3-3) won for the first time in four starts by scattering four hits, walking three and striking out one for the Cards, who took the first of a two-game series with the National League East leaders.
Eduardo Sanchez tossed a scoreless eighth and Fernando Salas nailed down his fourth save for the Cardinals, who marked the return of Manager Tony La Russa to the dugout by breaking a three-game losing streak.
La Russa had missed six contests while recovering from a case of the shingles.
Ryan Theriot and Nick Punto each had two hits and an RBI in the victory.
Cliff Lee (2-4) was saddled with the loss after allowing six walks and six hits over 6 1/3 innings, yielding three runs.
Ben Francisco drove in the Phillies' only run.
Notable deaths of 2014 [PHOTOS]
Arizona Cardinals player formally charged