Seattle trailed 5-2 after seven innings but got a two-run homer from Robinson Cano in the eighth.
Martin then drove a 1-2 pitch deep over the wall in right-center for his ninth home run.
Montgomery (2-0) wasn't charged with the runs and finished the game with 3 1/3 scoreless innings.
Cano put the Mariners up 1-0 in the first, following a one-out single by Seth Smith with an RBI double to left-center.
Crisp brought the A's even in the third with his fourth homer, a one-out solo shot to right off Nathan Karns.
BETTER OUTING FOR GRAVEMAN
Oakland starter Kendall Graveman allowed two runs on seven hits in 4 1/3 innings, but that was an improvement over his previous five starts in which he was 0-5 with a 7.92 ERA.
A's: 2B Jed Lowrie, on the DL with a bruised shin, was 1 for 4 in a rehab appearance on Monday for Triple-A Nashville. He is scheduled to be activated Wednesday and in the lineup. "I think as far as the psychology goes, we've been subtracting, and now we're on the verge of having a couple additions," manager Bob Melvin said. "I think that will certainly be welcome. I know Jed's looking forward to getting back in the lineup."
Mariners: SS Ketel Marte said his injured left thumb continues to improve, but he's being cautious. "It's better than yesterday," said Marte, who is on the 15-day DL. "It's hard, because I want to play."
A's: Zach Neal will be called up Wednesday from Nashville to make his first major league start. The right-hander was 5-1 with a 2.53 ERA in seven starts with the Sounds. He was previously called up May 11 for one game and made his debut with three innings of relief against the Red Sox, allowing three runs on four hits in three innings.
Mariners: Right-hander Hisashi Iwakuma (2-4, 4.39 ERA) is 2-1 with a 4.07 ERA in four starts in May after going 0-3 in five starts in April. In his only start against the A's this season, he allowed just one run on four hits in seven innings in an 8-2 victory.