Batting out of the nine hole, Conger later singled in another run to complete the scoring for the Astros.
Conger has played in 58 games this season, batting .220 with 10 homers and 27 RBI.
Houston starter, Collin McHugh worked 7 1/3 scoreless innings, scattering seven hits and striking out six. He improved to 15-7 with a 3.75 ERA.
The Astros increased their lead over second-place Texas to three games, thanks to the Angels' 5-2 win over the Rangers.
Minnesota will try to even the series in game two of the three-game series in Houston on Saturday at 7:10 pm EDT.
Anthony Rizzo highlighted an eight-run fifth inning with a grand slam, his 28th long ball of the season, sending the Cubs past the Diamondbacks, 14-5, in the opener of a three-game series at Wrigley Field in Chicago.
Rizzo upped his RBI total to 83 on the year but the Cubs could not make up any ground on the Pirates, who are currently four games to the good in the race for the first wild card and home field for the one-game playoff.
In the opener of a three-game series in St. Louis, the Pittsburgh Pirates set off a barrage of 17 hits in a 9-3 rout of the NL Central division leaders, but still trail the Cardinals by 5 1/2 games.
In the race for the second wild card, Chicago has a healthy 7 1/2 game lead over the Washington Nationals, who have moved past the slumping Giants, losers of seven straight.
Game two of the series in Chicago is slated for a 2:20 pm EDT start.