Minor (10-5) gave up four hits with no walks in seven innings. His sharp performance came two days after Tim Hudson was lost for the season with a broken right ankle.
The Atlanta rotation also is without left-hander Paul Maholm, who isn't on the disabled list but is expected to miss at least one start because of a bruised left wrist.
Wainwright (13-6), the NL leader in wins, took his first loss since a 2-1 decision to Texas on June 23.
Yadier Molina gave St. Louis a 1-0 lead with his eighth homer in the second inning. The Braves answered with two runs in the bottom of the inning.
Wainwright allowed four runs, three earned, on seven hits and one walk in seven innings.
Minor, who became the first Braves pitcher to reach 10 wins, lowered his ERA to 2.89. His strong start was especially important after Hudson's season ended when he was injured on Wednesday night against the Mets.
The Braves took a 2-1 lead with four hits off Wainwright in the second. Brian McCann doubled, moved to third on Dan Uggla's single and scored on Chris Johnson's single to left field. Minor added a single with two outs to drive in Uggla.
Heyward pushed the lead to 3-1 with his eighth homer, a one-out shot to left field, in the fifth.
With one out in the seventh and Johnson on first base following his second hit, Joey Terdoslavich pinch-hit for Minor and hit a grounder to shortstop Pete Kozma, who threw wild toward second base. Johnson scored on the error.
Heyward, sprinting toward the infield from right field, made a diving catch to take a hit away from David Freese in the fifth inning. Heyward rolled and came up holding the ball as Minor slapped his glove in approval on the mound.
NOTES: Of Minor's 103 pitches, 70 were strikes. ... Attendance was 50,124, a sellout. ... Hudson had surgery to repair his broken right ankle. His wife, Kim, said on her Twitter account the procedure went well. ... RHP Brandon Beachy, recovering from right elbow ligament-replacement surgery in June 2012, will come off the DL to take Hudson's rotation spot Monday night against Colorado. ... Cardinals LHP John Gast had season-ending surgery on his left shoulder. He could return in eight to 12 months. Gast was 2-0 with a 5.11 ERA in three starts before he was placed on the disabled list on May 26 with a left shoulder strain. ... Atlanta's Julio Teheran will face Joe Kelly in a matchup of right-handers on Saturday. Kelly will make only his fourth start of the season.
Link to box score: Atlanta 4, St. Louis 1
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