The Rangers, beset by injuries and struggling to score runs, lost for the third time in four games.
It was a 1-1 contest heading into the sixth, but the Blue Jays loaded the bases with nobody out in that inning when Munenori Kawasaki was hit by a pitch, Melky Cabrera singled and Jose Bautista drew a walk.
That brought up Encarnacion, whose double to center delivered Kawasaki and Cabrera. Sacrifice flies from both Adam Lind and J.P. Arencibia accounted for the other two runs in the inning.
Toronto's Esmil Rogers, who has spent most of his five-year career as a reliever, was given his second start in five days and held the Rangers to a run on three hits with six strikeouts in four innings.
Rogers was removed, however, after throwing 73 pitches and Aaron Loup came on to strike out four of the five men he faced.
The win credited to Neil Wagner (1-0), who picked up his first major league victory in 11 career appearances. He gave up a hit and struck out one in 1 1/3 innings as the third of five Toronto pitchers.
All six Toronto runs were surrendered by Nick Tepesch (3-5) on just five hits over seven innings.
Couple calls 9-1-1 over missing hash browns; assault McDonanld's employees
Britney Spears debuts 'Perfume' video