Athletics shortstop Cliff Pennington threw wide on a double-play ball, allowing Gutierrez to score from second and snap a 2-2 tie. Adam Kennedy then doubled to bring Brendan Ryan in from second with an insurance run.
Brandon League (1-4) came away with the win and a blown save in relief of Felix Hernandez, who struck out 10 in his eight-inning performance.
Trevor Cahill gave up two runs -- one earned -- in seven innings. Andrew Bailey (0-1) was on the mound in the 10th and took the loss.
The miscue in the 10th spoiled a comeback in which the A's scored single runs in the bottom of the eighth and ninth innings to tie the game. Kurt Suzuki homered in the eighth and Coco Crisp tied it with a one-out RBI single.
The Mariners took a 2-0 lead with a run on Carlos Peguero's sacrifice fly in the second and a solo home run by Dustin Ackley in the seventh.
Swim Week Miami Beach 2014 [PHOTOS]