It was the third straight win for the Rays and came in dramatic fashion after Toronto had tied it up in the eighth.
Aaron Loup (4-6) came on to work the ninth for the Blue Jays and struck out Sean Rodriguez to open the inning.
Escobar then drew a walk and scored when Lobaton drove the ball to deep right. Lobaton had also singled in a run in the third.
Toronto led by two heading into the bottom of the sixth, but Matt Joyce homered in that inning to bring Tampa Bay within one and the Rays moved in front in the seventh on an RBI groundout by Escobar and a go-ahead RBI single from Sam Fuld.
Fernando Rodney (5-3) gave up two runs in the top of the ninth, but escaped the jam to pick up the win.