Both sides were limited to four hits and the Rangers failed to take advantage of a potentially game-changing Toronto fielding error in the seventh.
The Blue Jays snapped a three-game losing streak.
Encarnacion's 31st homer of the season came off Yu Darvish (12-9), who took the loss despite giving up just three hits and striking out 10 over seven innings. A single by Rajai Davis in the fifth accounted for the third Toronto run.
Trailing 3-1 heading into the seventh, the Rangers loaded the bases with two out and they scored a run when second baseman Omar Vizquel committed a fielding error on a grounder from Mike Olt.
That brought up leadoff man Ian Kinsler, but he left the bases loaded by hitting a fielder's choice grounder to shortstop.
J.A. Happ (9-10) surrendered only one earned run on two hits over six innings and a parade of five members of the Toronto bullpen then gave up two more hits the rest of the way.
Casey Janssen worked a perfect ninth for his 16th save.