The Rays had run off seven consecutive wins to take the lead in the three-team fight for the American League's two wild card berths, but they had only a one-game advantage over Cleveland beginning the night.
Tampa Bay took a quick 2-0 lead, but the Blue Jays scored four times in the fourth to take control.
Jose Reyes singled off Jeremy Hellickson to open the fourth and was sacrificed to second. Tampa Bay third baseman Evan Longoria then misplayed a grounder off the bat of Brett Lawrie to put runners on first and second.
Moises Sierra and Anthony Gose both singled in a run to tie the game before Goins sent a shot to center that brought home Sierra with the go-ahead run. When center fielder David DeJesus let the ball get past him for an error, Gose came in as well.
Hellickson (12-10) took the loss, surrendering three earned runs on six hits in 4 2/3.