Rays shortstop Matt Duffy delivered the big blow in a five-run sixth with a three-run double off the wall in left field. Logan Forsythe added three hits and scored a run, Kevin Kiermaier homered and everyone in the the Rays' lineup reached base at least once.
The Blue Jays rallied in the ninth, scoring four runs before Alex Colome retired Edwin Encarnacion on a fly ball to left as the potential go-ahead run to lock up his 30th save.
Right-hander Marco Estrada took the loss for Toronto after he allowed five runs on seven hits and two walks over five-plus innings.