Alex Rios homered for Toronto, which has been riddled with injuries. Staff ace Roy Halladay was whisked to hospital before the game for an appendectomy, sidelining him for four to six weeks. Third baseman Troy Glaus suffered an apparent leg injury while running out a fly ball in the first inning and was replaced by Jason Smith in the second inning.
Glaus missed 14 games earlier this season because of a sore left heel.
Burnett (3-3) allowed one run and five hits with a season-high five walks in 6 2-3 innings. He picked up his first win since beating the New York Yankees on April 26.
Rios hit a solo homer to left in the seventh, his seventh. Vernon Wells followed with a double and scored on Smith's single to make it 5-1.
Elijah Dukes homered in the first for Tampa Bay. It was his sixth of the season and third in the last seven games. He also homered the Devil Rays' 11-6 loss Thursday night at Baltimore.
Toronto went in front with a two-out rally in the fourth. Aaron Hill and Lyle Overbay singled before Jason Phillips hit a two-run double to center to make it 2-1.
Phillips' double gave the Blue Jays their first lead since they led 1-0 in the fifth inning of last Sunday's 3-2 loss at Texas.
Carlos Pena's fielding error in the sixth allowed Hill to score Toronto's third run.
Scott Kazmir (2-2) lost for the first time since April 8, giving up five runs, four earned, and nine hits over 6 1-3 innings. He struck out six and walked three. Both of Kazmir's losses this season have come against Toronto.
The Devil Rays matched a season high with four stolen bases. ... Wells scored his 500th career run.
Carl Crawford was the only Devil Rays with multiple hits in the loss. He finished the night 2-4 to raise his batting average to .297, but also struck out to end the game. Crawford also collected two of the Ray's 4 stolen bases, a season high.
Infielder Josh Wilson, who was recently claimed off waivers from the Washington Nationals, did not appear in the game. Ben Zobrist was sent down to AAA Durham in order to make room for Wilson on the roster. In 15 games in a reserve role for the Nationals, Wilson was batting .053 (1-19) with five errors.
One positive in tonight's game was the strong performances from Shawn Camp and Gary Glover. Camp gave up two hits in the seventh inning, but was able to retire the side without allowing any runs. Glover pitched a scoreless eighth, but his ERA is still 7.00 for the season.
Although Dukes did connect for a long homerun off of Burnett in the first inning, the Tampa native also struck out three of his four other at bats. Dukes, who finished the night 1-5, is still hitting only .214.
Tyler Hissey contributed to this story.