Munoz celebrated a rare start with a home run and a triple to help the Cardinals beat the Cincinnati Reds 3-1.
Munoz, making his 16th start among 55 games, also singled to finish with three of the six hits for the Cardinals, who improved to 7-3 since the All-Star break.
"I try to prepare myself to come into any situation that (manager Mike) Shildt puts me in," Munoz said through an interpreter. "I try to have a good game, so he'll trust me more."
His second homer of the season in the ninth, off Raisel Iglesias, gave St. Louis an insurance run.
"He takes the right approach," Shildt said. "He's got the ability to change his approach during an at bat."
The Reds avoided their ninth shutout loss of the season on Phillip Ervin's eighth-inning pinch-hit home run off Andrew Miller.
Just two Reds baserunners got as far as second base in the first four innings against Jack Flaherty, who was 0-3 over his last 10 starts since winning at Atlanta on May 14, before they loaded the bases with nobody out in the fifth.
Flaherty got Yasiel Puig to pop out, and Giovanny Gallegos (2-1) came on to fan Josh VanMeter and Scooter Gennett, the first two of four straight strikeouts.
"When I'm in the bullpen, I just try to be ready for any situation," Gallegos said. "I just come in and try to throw strikes. I try not to think too much. I just try to make good pitches."
"That was a tough spot," Shildt said. "Then he goes out and has a big sixth, too."
"You get in that situation, it's a competition," Reds manager David Bell said. "The Cardinals won that competition. It turned out that was the difference in the game."
Carlos Martinez pitched the ninth for his eighth save.
Anthony DeSclafani (5-5) struck out a career-high 11 and allowed just one earned run in six innings, but a shaky second was all the Cardinals needed.
Four different Cardinals stole bases while St. Louis was scoring two runs in the inning. Tyler O'Neill scored from third on Munoz's one-out bloop single to right over a drawn-in Cincinnati infield. Andrew Knizer walked and, after a double steal, Munoz scored an unearned run on Suarez's error of Harrison Bader's sharp one-hopper.
"Anthony pitched as well as he possibly could," Bell said. "That inning cost him for sure."
"I have to be more aware of the runners," said DeSclafani, who allowed four hits and no walks. "That falls on me."
CARDINAL MOVES
Following Saturday's game, the Cardinals optioned RHP Dominic Leone and RHP Ryan Helsley to Triple-A Memphis and replaced them on Sunday with INF Rangel Ravelo and LHP Tyler Webb.
THROWBACK NO. 9
The Reds on Sunday wore replicas of the uniforms worn by the 1961 National League champions, the ninth of the 15 throwback uniforms they are wearing this season to help celebrate the 150th anniversary of baseball's first all-professional team. The jerseys were sleeveless, and many players went without T-shirts underneath, including Derek Dietrich and Michael Lorenzen, who were spotted lifting weights in the dugout.
PUNCHOUT
Reds pitchers finished with a season-high 15 strikeouts, the most since they struck out 18 Brewers on May 30 of last season.
TRAINER'S ROOM
Reds: OF Nick Senzel was expected to start on Sunday after pinch-running and playing defense on Saturay, but manager David Bell chose to have him avoid a full day in 90-degree weather and not risk the right hamstring that tightened on Wednesday.
UP NEXT
Cardinals: The Pirates roughed up RHP Daniel Ponce de Leon (1-0) for eight hits and four runs in 3 2/3 innings of a 6-5 St. Louis win on Wednesday.
Reds: RHP Sonny Gray (5-6) allowed four hits in eight shutout innings of a Cincinnati 3-0 win over Milwaukee on July 3.
