Houston won the opener 6-2 and put a damper on the first series of Derek Jeter's final season. Jeter was 0 for 3 with a walk and a strikeout.
Fowler's leadoff homer put Houston up and he scored the second run after his triple in the third.
The Yankees scored in the seventh before the Astros added an insurance run with Dominguez's homer in the bottom half.
Jarred Cosart (1-0) allowed four hits in five scoreless innings and Josh Fields pitched a perfect ninth for the save.
Hiroki Kuroda (0-1) yielded three hits and two runs with five strikeouts in six innings.
The offseason trade for Fowler has paid immediate dividends for Houston. The longtime Colorado player had a pair of doubles on Tuesday night and is now the first player in franchise history with two extra-base hits in each of his first two games with the team.
The Astros were up 2-0 in the seventh when Yangervis Solarte grounded into a double play with runners at first and third that Brett Gardner scored on to cut the lead to 2-1. It was the first major league plate appearance for Solarte.
The two-out homer by Dominguez off David Phelps landed about three rows up in the right field stands to stretch Houston's advantage to 3-1.
Carlos Beltran doubled off Matt Albers on the first pitch of the eighth inning before Albers struck out the next three Yankees.
Cosart allowed just two singles through four innings. He ran into some trouble in the fifth and after consecutive one-out singles by Gardner and Brian Roberts. He escaped the jam when Kelly Johnson grounded into a force out before he retired Jacoby Ellsbury.
Jerome Williams made his Astros debut when he replaced Cosart for the sixth. He walked Jeter on four pitches and Brian McCann singled on a sharp grounder with one out to leave runners at first and third. But he retired the next two to end the threat.
Fowler's leadoff homer came a day after he started his Astros' career with a leadoff double. Houston's next hit came on Fowler's standup triple which bounced off the wall in right-center with one out in the third.
Robbie Grossman reached on an error by first baseman Teixeira when his grounded bounced off Teixeira's glove, allowing Fowler to score and make it 2-0.
New York turned a double play to end that inning and Houston didn't have another baserunner until Grossman hit his first career triple with one out in the sixth. But Kuroda ended his night by retiring the next two to end the inning and leave Grossman stranded.
The Yankees intentionally walked Jose Altuve to load the bases with two outs in the eighth. Houston came up empty when pinch-hitter Carlos Corporan grounded out.
NOTES: Andy Pettitte threw out the ceremonial first pitch before the game. ... Jeter, who announced in February that he was retiring, got a pair of cowboy boots with Yankees' pinstripes, a 10 gallon cowboy hat and a set of golf clubs as the Astros honored him in a pregame ceremony Wednesday night. Pettitte and Roger Clemens participated in the tribute.