Clinging to a 4-3 lead late in the game, the Mariners exploded for six runs to win going away.
Jaso, whose second-inning shot put Seattle ahead to stay, made it 5-3 in the eighth with a single that chased home Kyle Seager. The Mariners ended up sending 11 men to the plate in the frame, which featured five hits, an error and a wild pitch.
Seager finished 3-for-5 while Michael Saunders added three hits and Dustin Ackley went 2-for-4 with an RBI for the Mariners, who evened their three-game set against the Rangers.
Jason Vargas (6-4) went 6 2/3 innings to earn the victory, allowing three runs on five hits while walking three and striking out two.
Rangers starter Scott Feldman (0-3) was touched for four runs (two earned) on four hits over four full frames.
Josh Hamilton belted his MLB-best 21st homer, a two-run shot, ending with three RBI for American League West-leading Texas.