The Mariners took a two-run lead in the 10th before Tom Wilhelmsen survived a shaky save in the bottom half of the inning.
Wilhelmsen gave up an RBI single to Dewayne Wise and had the bases loaded before finally retiring Tyler Flowers on a strikeout to end the contest.
Seattle struck for five runs in the fifth to take a 6-1 lead, Gutierrez highlighting the inning with a two-run double. Chicago came back with four runs in the same inning, Alejandro De Aza contributing a two-run homer and Alex Rios hitting a solo shot.
Chicago tied it at 6-6 in he seventh when a ground out by Rios delivered Gordon Beckham from third.
Kameron Loe (1-0) worked the ninth inning to get the victory, throwing just seven pitches. Nate Jones (0-1) gave up the 10th-inning runs in the second of his two innings of work.