McHugh (1-0), called up from Triple-A Oklahoma City for the start, struck out the first three batters of the game to set the tone for his first win in 10 career starts. The right-hander didn't walk a batter, giving up three hits in 6 2-3 shutout innings.
Josh Fields pitched the ninth for his second save. The Astros have won six straight against the Mariners.
Justin Smoak provided Seattle's only offense with a two-run homer in the seventh inning as the Mariners extended their losing streak to eight games.
McHugh completely shut down Seattle, only allowing one runner to reach second base. His 12th strikeout came against Robinson Cano to leadoff the seventh, but Houston manager Bo Porter brought on reliever Raul Valdes with two outs in the inning. He walked Kyle Seager and then gave up Smoak's two-run home run.
That was a rare bright spot for the Mariners, who struck out 14 times, equaling their season high set Monday.
Seattle starter Erasmo Ramirez (1-3) had a decent outing of his own, striking out eight over six innings. Ramirez only allowed three hits, but two of them were homers giving the Astros a 3-0 lead after two innings.
Three at-bats into the game, Castro just cleared the left field wall for a two-run homer, his fourth. Carter followed in the second inning with a shot to left that landed in the second deck for his first homer of the year.
Seattle's Dustin Ackley tried to counter with his own deep ball to left in the bottom of the second, but Dominguez made a leaping catch at the wall to end the inning.
Carter's bases-loaded single gave Houston an insurance run in the eighth.
NOTES: The crowd of 10,466 was the fifth-lowest in Safeco Field history. Six of the seven lowest crowds at Safeco have been matchups with the Astros, all coming since the start of last season. ... Seattle RHP Hisashi Iwakuma (finger) was scheduled to pitch in a rehabilitation assignment at Triple-A Tacoma, but instead threw a simulated game at Safeco Field on Tuesday afternoon due to weather concerns. Mariners manager Lloyd McClendon said the outing went well, and Iwakuma will have a rehab outing with Tacoma on Sunday. ... Astros RHP Lucas Harrell, designated for assignment on April 16, cleared waivers and was outrighted to Triple-A Oklahoma City.