Jaso rapped a two-out single in the sixth inning that broke a 3-3 tie and gave Seattle its longest winning streak since they won eight straight in 2007.
Eric Thames tied the game in the fifth with a two-run homer for the Mariners. Dustin Ackley had Seattle's other RBI.
Blake Beaven (7-6) earned the win, allowing three runs on seven hits over 7 2/3 innings. Tom Wilhelmsen pitched the ninth for his 15th save.
Carlos Villanueva (6-1) took the loss for the Blue Jays, who have dropped four consecutive games. Villanueva lasted six innings, giving up four runs on seven hits.
Celebrity Families of 2014 [PHOTOS]