St. Louis, which set a season high both for runs in an inning and in a game, won for the eighth time in its last 12.
Milwaukee has lost three of five.
Westbrook (3-1) gave up seven hits, struck out five and did not walk a batter. He has allowed two earned runs or less in all four of his starts this season.
Gallardo (1-2) lost for the ninth time in 10 regular-season starts against St. Louis. He has a 7.05 ERA in 13 starts against the Cardinals and has given up eight earned runs twice.
Carlos Beltran and David Freese drove in Jay and Holliday to start the eight-run outburst. Yadier Molina drew a walk and Carpenter ripped a 3-2 pitch off the center-field wall to push the lead to 6-1. Schumaker followed with a run-scoring hit and Jay added a two-run single. Holliday capped off the frame with a run-scoring single to right.
St. Louis last scored eight runs in the fifth inning of a 13-5 win over Chicago on July 30, 2011.
The Cardinals have scored nine runs or more five times this season.
St. Louis starting pitchers have recorded 12 wins the season, the highest total in both leagues.
The Cardinals have outscored their opponents by an NL-leading 49 runs this season.
Notes: Milwaukee had given up the first run in its previous eight games before scoring in the top of the first Friday. ... Molina will be presented with his fourth consecutive Gold Glove award prior to Saturday's game. ... Kyle Lohse (3-0, 0.99 ERA) will face Milwaukee's Marco Estrada (0-0, 2.45) in the second game of the three-game set on Saturday. ... The Cardinals, who began a six-game homestand Friday, played 13 of their first 19 games on the road.
Link to boxscore: St. Louis 13, Milwaukee 1