The game was tied 1-1 in the 10th when Lobaton came up to face Brad Lincoln (1-2) with one out and smashed a 2-1 pitch deep into the right-field stands for the decisive blow.
Lobaton also provided a ninth-inning, game-winning triple in Friday's 5-4 win over the Blue Jays.
Jake McGee (3-3) was credited with the decision after scoreless top of the 10th, following seven innings of one-run ball from starter Chris Archer.
Evan Longoria went 2-for-3 with a bases-empty blast for the second-place Rays, who took the rubber match of a three-game set. They came into the contest trailing American League East-leading Boston by two games.
Edwin Encarnacion connected on a solo homer for Toronto.