The Mariners trailed 4-2 after four innings but tied it up in the fifth on an Ichiro Suzuki RBI and a run-scoring wild pitch uncorked by Giants starter Tim Lincecum (2-8).
Gutierrez, batting for John Jaso, grounded a pitch to deep third base and beat out Joaquin Arias' throw, allowing the go-ahead run to score, while Brendan Ryan followed with a two-run single to ice the game.
Hisashi Iwakuma (1-0) earned the win with two scoreless relief frames and Tom Wilhelmsen collected his fourth save as the Mariners evened the three-game series.
Montero finished 3-for-4 with an RBI, while Casper Wells socked a solo homer for the Mariners.
Lincecum, meanwhile, extended his winless streak to nine starts, yielding five runs on five hits over five frames as his ERA rose to 6.19.
Ryan Theriot went 3-for-5 with two RBI singles for San Francisco.