Lind provided a score-tying RBI single in the third inning and broke a 1-1 deadlock with a two-run hit in the fourth against reliever Alex Torres (4-2) that put the Blue Jays head to stay.
Ryan Goins and Kevin Pillar each belted a two-run homer for Toronto.
Happ (5-7) controlled the Rays on one run over 7 1/3 innings, allowing five hits with a walk while striking out four.
Wil Myers and Delmon Young each supplied an RBI for Tampa Bay, which dropped a second straight following an eight-game winning streak.
The loss dropped the Rays into a tie with the Texas Rangers for the second and final American League wild-card spot with one game remaining.
2014: The Year in Music [PHOTOS]