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.
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.
Asked if he felt he needed to step up as the staff ace, Minor said, "That's not really my role. I go out every fifth day and just try to pitch.
"With Huddy going down, that was our ace. That was our best guy. We just need everybody else to step it up a little bit."
The Atlanta rotation also is without left-hander Paul Maholm, who is expected to miss at least one start because of a bruised left wrist.
Braves manager Fredi Gonzalez also resisted suggestions that Minor is emerging as the top pitcher on a young staff that also includes rookies Julio Teheran and Alex Wood.
"Let's not get there yet," Gonzalez said.
"Mike Minor doesn't have to do anything. He's been this good for a while. We saw him growing up and getting better and better about this time last year. Let's let him dictate his own career and let's not start putting labels yet."
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. He complimented the Braves hitters on their patience in trying for opposite-field hits.
"I think I just have to tip my hat," Wainwright said. "I think they had a great approach from the first pitch of the game on.
"They took some great at-bats off me, worked the counts, and they didn't get pull-happy out there. Really, they hit some tough pitches and worked some tough at-bats. Sometimes you just get beat. I had some pretty good stuff tonight."
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.
"I got a pitch to hit," Heyward said before adding that Wainwright "made a mistake with a changeup away."
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.
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. ... Teheran will face Joe Kelly in a matchup of right-handers on Saturday. Kelly will be making his fourth start of the season.
Copyright by STATS LLC and The Associated Press
ATLANTA, GA - JULY 26: Mike Minor #36 of the Atlanta Braves pitches against the St. Louis Cardinals at Turner...