Saunders (11-13) allowed just one unearned run on six hits over 5 1/3 innings, while Carter Capps, Yoervis Medina and Danny Farquhar kept the Astros off the board the rest of the way.
"We had opportunities offensively and misplayed some balls defensively, (but) in the end we won the ball game," Mariners manager Eric Wedge said.
Kendrys Morales, Nick Franklin and Dustin Ackley all pushed a run across in the first inning against Dallas Keuchel.
Morales singled in Brad Miller, Franklin worked a bases-loaded walk and Ackley hit into a run-scoring groundout to cap the productive frame.
Keuchel (5-8) faced the minimum from the second through the seventh innings, but the only run of support he got came in the fourth when Brandon Barnes scored on a Nick Franklin error.
Cody Clark had two chances with runners in scoring position but bounced into an inning-ending fielder's choice with the bases loaded in the second, then grounded out to short to leave runners on second and third in the fourth.
Farquhar worked around a leadoff walk in the ninth to post his 11th save and hand the Mariners their third straight win to open this four-game set.
The Astros finished 0-for-8 with runners in scoring position and have managed a mere eight runs during their five-game slide.
"We just can't seem to be able to get the big hit," Astros manager Bo Porter said.
Neither team recorded an extra-base hit ... Keuchel struck out eight over seven innings and was charged with three runs on four hits and two walks ... Saunders had pitched to a 7.71 ERA over his previous seven starts ... The Mariners have won five straight road games for the first time since winning six in a row from April 17-30, 2011 ... Seattle leads the season series, 10-5.
09/01 02:48:39 ET