On Thursday, they finally put together a complete game and won 6-1 to avoid a series sweep.
Dominguez snapped an 0-for-23 skid with his two-out shot to left-center field off Mike Minor (2-5) that made it 5-1 in the fifth inning.
"That's the big hit that when we were in this here funk that we were in, that was the big hit that had been eluding us," manager Bo Porter said.
Dominguez said there was a mixture of relief and excitement when he connected on his home run.
"I try not to focus on it but of course it gets in your head," Dominguez said. "Good situation. Got a good pitch to hit and I was finally able to put the barrel on it."
Cosart (8-5) allowed six hits and a run for his fourth straight victory. Porter believes that Cosart's presence on the mound has improved with each start this season and the 24-year-old agreed.
"When I'm throwing strikes I have a lot more confidence and obviously that's what they've been preaching," Cosart said. "And with the mechanical stuff I've been doing I have a lot more confidence in throwing strikes and just being able to trust my stuff and attack the hitters and know I've got a really good defense behind me that's going to make a lot of plays for me."
Springer's solo homer off Juan Jaime in the seventh pushed the lead to 6-1. He has 15 homers this season, the most by a rookie in franchise history before the All-Star break. Lance Berkman had the previous mark with 12 in 2000.
Minor gave up seven hits and five runs in six innings to remain winless since May 19.
Jon Singleton had two hits and an RBI and Jose Altuve added a pair of hits and swiped two bases for the Astros, who had managed just four runs combined and had been shut out twice in a four-game losing streak. Altuve leads the American League with 107 hits and 30 steals.
"Things just didn't go our way," Justin Upton said. "For the most part we tried to play a little small ball with our run-scoring struggles and we've done a pretty good job of it. [Thursday] it didn't work out for us and we didn't get the big ball, either."
The Braves had trouble stringing together hits against Cosart and he was helped by the Astros turning a pair of double plays. Evan Gattis doubled to start the seventh before Jason Heyward drew a walk, but Cosart retired the next three batters to end the threat.
Altuve singled and a double by Singleton, which bounced off the wall in left field, sent him home to tie it at 1-1 in the first.
Minor plunked Dominguez to start Houston's fourth before a double by Castro. The Astros took a 2-1 lead when Castro scored on a groundout by Jesus Guzman.
The Astros opened their gates 30 minutes early Thursday to allow fans to watch the World Cup match between the United States and Germany on the stadium's big screens. ... Atlanta 1B Freddie Freeman was back in the lineup after leaving Wednesday night's game in the eighth inning after being hit by a pitch on the right elbow. ... Houston selected the contract of RHP Jose Veras from Triple-A Oklahoma City and outrighted RHP Kyle Farnsworth before the game and he has elected free agency. Veras struck out Justin Upton for the last out of the game.