The Blue Jays trailed 4-1 after two innings but narrowed the deficit to one run in the seventh when Colby Rasmus smacked a two-run homer.
Then in the ninth, Joel Peralta (0-2) took the mound and with one out, Izturis belted the first pitch he saw into the first row of the left-field stands for a 5-4 lead.
Melky Cabrera (3-for-5) added an insurance run with an RBI double for Toronto, which overcame a seven-run deficit to stun the Rays in Monday's first contest of the four-game series.
Reliever Steve Delabar (3-1) earned the win with two shutout innings and Casey Janssen notched his ninth save for the Blue Jays.
Toronto starter J.A. Happ went 1 1/3 innings before being struck on the head with a line drive off the bat of Tampa Bay's Desmond Jennings. He was taken off the field on a stretcher.
The ball bounded into right field and two runs scored on the play, with Jennings reaching third for a triple.
Celebrity Families of 2014 [PHOTOS]