Minor allowed one hit, four walks and struck out seven. The lefthander threw 63 of 108 pitches for strikes. He left the game when Tyler Pastornicky hit for him in the seventh.
Atlanta manager Fredi Gonzalez thought Minor did a fine job in holding Colorado, which began the night second in the NL with a .272 batting average, hitless through six innings.
"They're not schleppers out there, and we've had some pretty good ball games pitched against them, with Tommy [Hanson] and Mike Minor and obviously [Kris] Medlen," Gonzalez said. "They swing the bats. They scare you a little bit."
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 3 1/2-game lead over the Los Angeles Dodgers in the NL wild-card race. The Braves had lost 11 of 17.
Atlanta continued to struggle offensively despite second baseman Dan Uggla and McCann returning to the lineup. Uggla was benched the last three games with a .208 batting average, and McCann missed the last three games after taking a cortisone shot in his right shoulder.
Uggla and McCann combined to go 0-for-7.
In other games *
At St. Louis, R.A. Dickey allowed two runs in 6 2/3 innings to improve to 18-4, and Ike Davis hit a three-run homer to lift the New York Mets to a 6-2 victory over the Cardinals.
* At Washington, Bryce Harper hit two homers and the Nationals went deep six times for the second consecutive game, making Gio Gonzalez (18-7) a winner in a 9-1 rout of the Chicago Cubs.
* At Pittsburgh, Kevin Correia (10-8) pitched six solid innings as a fill-in starter and Alex Presley, a late addition to the lineup, had two hits and scored three runs as the Pirates beat the Houston Astros, 6-3.
* At Miami, Rickie Weeks homered twice and drove in four runs to help Wily Peralta win his first major league start and lead the surging Brewers over the Marlins, 8-5. Corey Hart also homered and drove in four runs for Milwaukee, which has won 13 of 16 to climb within 6 1/2 games of St. Louis for the second wild card.
Dodgers No. 2 starter Chad Billingsley will miss the rest of the season after being placed on the 60-day disabled list because of elbow pain. The 28-year-old lefthander, who hasn't pitched since Aug. 24, was 10-9 with a 3.55 ERA in 25 starts.