Olivo's blast to left-center field in the sixth inning off Rangers reliever Joe Nathan was his first of the spring as the Mariners improved to 8-3-1. Montero added his double off Mark Hamburger in the seventh.
Rangers right fielder Nelson Cruz cranked his first home run in Cactus League play with a solo blast off Seattle starter Blake Beavan in the third, and left fielder David Murphy hit a solo shot off reliever Shawn Camp in the seventh.
"It was a good swing and a good feeling," Cruz said after his first extra-base hit of the spring. "Your work in Spring Training is about feeling. I'm feeling good, that's what matters."
Beavan, 23, continued his strong spring with five innings of two-run ball against his former team.
Acquired by the Mariners in the Cliff Lee trade in 2010, Beavan gave up just three hits and had no walks with two strikeouts. In three Cactus League starts, he's posted a 2.38 ERA (three earned runs in 11 1/3 innings) as he battles to earn a rotation spot.
"It's always good to face one of the best teams and best lineups in baseball," Beavan said. "It's hard to say you enjoy pitching against a team like that, but it definitely makes you concentrate a little more and realize when you miss. Good hitting teams like that are going to make you pay for it, as Cruz did on the fastball I wish I could have back."
Left-hander Matt Harrison went three innings for the Rangers (3-6) in his second Cactus League outing, giving up one run on three hits with two strikeouts. The lone run came on a blast by Mariners third-base prospect Vinnie Catricala in the third inning.
It was the second home run of Cactus League play for Catricala, 23, who also hit two in intrasquad games as well.
Murphy threw Ichiro Suzuki out on the plate on a close play in the sixth after Mike Carp singled to left following walks to Ichiro and Montero. But Olivo followed with his home run on a 1-1 count.
The Rangers also scored on a double by Michael Young in the fourth.
Up next for the Mariners: Hector Noesi continues his bid for a rotation spot with his second Cactus League start as the Mariners travel to Phoenix at 1:05 p.m. PT on Tuesday. The former Yankee threw two shutout innings against the A's on March 3. Closer Brandon League is also scheduled to pitch, along with Charlie Furbush, Shawn Kelley, Jeff Marquez and Sean Henn.