Bedard is the first Houston pitcher to go 6 1-3 hitless innings since Darryl Kile tossed a no-hitter against the Mets on Sept. 8, 1993.
Seattle manager Eric Wedge said it was the best he's ever seen Bedard, a former Mariner, pitch.
"Bedard threw a heck of a ballgame," Wedge said. "He had a great breaking ball going, a live fastball. He did everything good to keep us off-balance but we made him work. We were able to get him out of there at a reasonable time and try somebody else out."
Bedard didn't allow a baserunner until Kendrys Morales walked to start the fifth inning. But he got back on track after that, retiring the next four batters he faced.
He then issued consecutive walks to Saunders and Brad Miller with one out in the sixth inning. Saunders advanced to third and Miller took second on a passed ball by Jason Castro. Saunders scored on a sacrifice fly by Nick Franklin to get Seattle within 2-1.
A second passed ball by Castro allowed Miller to score and tie it at 2.
Raul Ibanez walked before Bedard retired Morales to end the inning.
Bedard retired Kyle Seager on a fly out before he was chased on a walk by Justin Smoak.
The Astros had runners at second and third with no outs in the third inning, but Iwakuma retired the next three batters, with two strikeouts to end the threat.
Matt Dominguez singled to start the fifth before a double by Jake Elmore. Dominguez scored on a sacrifice fly by Jose Altuve with one out to make it 1-0. A single by Castro sent another run home.
Seattle's tough offensive night ended its franchise-high streak of 23 straight games with a home run. It was the Mariners' first game without one since June 19.
NOTES: Seager went 0 for 4 to snap a 15-game hitting streak, which was the longest active streak in the majors. ... The series wraps up on Sunday when Seattle's Felix Hernandez (10-4) opposes Jordan Lyles (4-3). Hernandez leads the American League with a 2.53 ERA. ... Roger Clemens, the seven-time Cy Young Award winner and special assistant to Houston general manager Jeff Luhnow, was at Minute Maid Park on Saturday. He had a talk with the Astros pitching staff and tried to encourage them to stay positive as the losses continue to pile up.