Atlanta, which is second in the National League's East Division at two games behind Philadelphia, kept pace with the first-place Phillies on Friday when Freddie Freeman and Alex Gonzalez each had a home run and three RBI in an 11-4 victory.
Houston is last in the Central Division, 13 1/2 games behind St. Louis.
Tim Hudson (5-5) allowed two runs on seven hits while striking out four through six innings to earn the win, snapping an 0-3 streak over his past five starts.
Houston's Aneury Rodriguez (0-4) went four-plus innings, allowing six runs on six hits and a walk.
Michael Bourn tied his career high with four hits and was a home run short of the cycle in the Astros' sixth loss in seven games.
Braves hurler Mike Minor, the seventh overall pick in the 2009 draft, reached the majors last season and was 3-2 in nine appearances with a 5.98 earned run average across 40 2/3 innings.
He debuted this season with a 5-4 loss in Milwaukee on April 6 and has since followed it up with a no-decision at Pittsburgh on May 25 and a 5-4 loss against San Diego on May 31.
He's been touched for 22 hits and nine runs in his initial 16 innings this season, walking nine batters and striking out 11 while foes have established a .338 average against him.
Batters hit .314 against Minor in 2010.
For Houston, right-hander Jordan Lyles makes the third start of his rookie season.
Just 20 years old, Lyles was a supplemental draft pick of the Astros in 2008 and debuted at Wrigley Field when he allowed five hits and two runs while going seven innings against Chicago in a no-decision on May 31.
He dropped a 7-2 verdict on June 5 at San Diego in start No. 2, allowing five hits and four runs in four innings.
The 6-foot-4, 210-pounder began pitching in the minors at age 17 in 2008 and was 3-3 with a 4.23 earned run average in 15 starts with two teams.
He moved from Single-A to Triple-A between 2009 and 2010 and was 3-3 with a 3.20 ERA with Oklahoma City of the Pacific Coast League in 10 starts before getting called up to the majors.
Atlanta swept a two-game set against Houston from May 16-17 and has won nine of the last 10 encounters between the two ballclubs.