A two-run homer by Miguel Olivo in the eighth gave the Mariners some insurance and they went on to snap a four-game losing streak.
Texas stayed four games in front of Oakland in the American League West after the A's fell in 10 innings earlier in the evening to the New York Yankees.
David Murphy drove in all three Texas runs, two of them with a single in the fourth that rallied the Rangers from a 2-0 deficit.
Seattle immediately regained the lead, however, with Triunfel delivering the tiebreaking run. The RBI double was his second hit in the majors.
Hisashi Iwakuma (7-5) allowed three runs on eight hits over seven innings to get the win. Tom Wilhelmsen worked the ninth for his 28th win.
Martin Perez (1-2), making his first start since being placed in the Texas rotation, went four innings to take the loss. He gave up four runs, three earned on six hits.