Minor (8-10) lost a no-hit bid in the seventh when Jordan Pacheco led off with a single. Pacheco stole second, but was stranded when Minor struck out Ramon Hernandez, Chris Nelson on a foul tip and Andrew Brown looking.
The Braves made it 1-0 in the fourth off Alex White (2-8) when Chipper Jones led off with a single, moved to second when Freddie Freeman walked and scored when shortstop Josh Rutledge threw errantly to first after recording one out on Brian McCann’s fielder’s choice grounder.
Atlanta began the night with a two-game lead over St. Louis and a 3½-game lead over the Los Angeles Dodgers in the NL wild-card race. The Braves had lost 11 of 17.
Jose Constanza drew a leadoff walk in the seventh for Atlanta off Matt Ottavino, stole second and moved to third on Tyler Pastornicky’s sacrifice bunt.
Matt Reynolds and William Harris got the last two outs with strikeouts of Michael Bourn and Martin Prado.
White, who was facing the Braves for the first time in his career, allowed two hits, one unearned run and four walks with no strikeouts in four innings.
Atlanta continued to struggle offensively despite second baseman Dan Uggla and McCann returning to the lineup. Uggla was benched the past three games with a .208 batting average, and McCann missed the past three games after taking a cortisone shot in his right shoulder.
Uggla and McCann combined to go 0 for 7. The Nos. 2-4 hitters – Prado, Jason Heyward and Jones – each left three runners on base, but the Braves did manage to improve to 6-40 this year when scoring two or fewer runs.
Atlanta had lost 11 of 17 when scoring two runs or less.
Harris pitched the final 1⅓ innings for Colorado, helping the Rockies’ bullpen run their streak to 15 consecutive scoreless innings in the four-game series.
Facing Eric O’Flaherty in the eighth, Dexter Fowler walked with one out and advanced to third on Rutledge’s single. After O’Flaherty struck out Carlos Gonzalez and Rutledge stole second off Kimbrel, the Atlanta closer struck out Pacheco to end the threat.
Kimbrel earned his 32nd save in 35 chances. In the ninth, he struck out Hernandez and pinch-hitter Tyler Colvin. After pinch-hitter Jason Giambi walked, Wilin Rosario struck out to end the game.
Minor, who singled in the second, improved to 2-3 with a 2.98 ERA in his last seven starts. In his first career start against Colorado on May 5 in Denver, Minor allowed 10 hits and eight runs but received no-decision in the Braves’ 13-9 win.