Kendrick (1-1), who entered with a 7.61 earned-run average in five starts this season, gave up six hits and two walks in seven scoreless innings for the Phillies, winners in four of their last five.
Danys Baez and Jose Contreras each hurled a perfect inning of relief to close out the shutout, the fourth of the season for Philadelphia
Brad Penny (3-2) lost his second straight start by allowing three runs on five hits while fanning six in as many innings for the Cardinals, who have totaled one run in back-to-back losses following an 8-1 stretch.
Victorino opened the bottom of the fourth with a single — the first baserunner for the hosts — and Polanco followed with a blast into the first row of seats in left-center for a 2-0 game.
Victorino tacked on another run with a leadoff shot to right in the sixth.
In the seventh, David Freese singled and moved to third when Brian Schneider threw away pinch-hitter Jon Jay’s one-out dribbler in front of the plate. The Cardinals’ best opportunity to score was thwarted when Brendan Ryan bounced into a 6-4-3 double play.
Juan Castro beat out an infield single in Philadelphia’s turn before exiting with a left hamstring strain. Wilson Valdez relieved Castro on the basepaths and raced home on Greg Dobbs’ pinch-hit double to the gap in right.
The Phillies will turn to ace Roy Halladay for the series win on Thursday afternoon, while the Cardinals counter with Kyle Lohse…Jayson Werth went 0- for-3 with three stikeouts, ending his streak of 26 straight games reaching base safely…Kendrick is 4-0 in his career against St. Louis…Cardinals starters have strung together a streak of 14 consecutive quality starts, the most for the franchise since the 1973 season.