Dickey (7-8) retired the first 13 batters he faced, recording five of his six total strikeouts in that span.
James Loney broke up the no-hit bid with a one-out single in the fifth. Dickey allowed a single to Yunel Escobar in the sixth and a walk to Desmond Jennings in the seventh. No other Tampa Bay player reached base.
Tampa Bay starter Roberto Hernandez (4-9) also pitched well but was touched for six hits and all three Toronto runs. He struck out five and walked one in eight-plus innings.
Jose Bautista led off the Blue Jays fourth with a double and scored on a two-out base hit by Melky Cabrera. Adam Lind hit a two-out home run in the sixth and Edwin Encarnacion led off the ninth with his 22nd home run, a shot that chased Hernandez from the game.
Dickey and Hernandez combined to complete the game in a brisk 2 hours, 10 minutes.