Shields (8-6) gave up four hits, two walks and had four strikeouts for Tampa Bay, which started Friday a half-game behind AL East-leading Boston.
Grant Balfour got the final four outs for his fourth save.
Six of Tampa Bay's losses during the skid came on the road. Friday's victory improved the Rays' home record to 37-14.
Burnett also went seven innings, giving up two runs and five hits. He had won his two previous starts.
Toronto has lost six of seven games against Tampa Bay this season.
Adam Lind put the Blue Jays ahead 1-0 on a solo homer in the third. He has four homers and 17 RBIs in 18 games since being recalled from Triple-A Syracuse on June 21.
Tampa Bay went 5-for-53 with runners in scoring position over the previous seven games and failed to convert on five more chances during the first two innings. They didn't have any chances with runners on after that.
Rays principal owner Stuart Sternberg talked with his team before batting practice. Tampa Bay finished in last place nine times in its first 10 years.
"We have a chance for an incredible two months," Sternberg said.
Notes:@ Blue Jays RHP Shaun Marcum (right elbow) is expected to be activated from the 15-day disabled list to start Tuesday's game at Baltimore. ... Rays LF Carl Crawford stopped a career-long 0-for-26 slide with a single in the third.... Tampa Bay activated RHP Al Reyes (shoulder) from the DL. ... Toronto RHP Dustin McGowan (shoulder) will have his status re-evaluated in two weeks. ... Burnett became the first Toronto pitcher to start consecutive games. He also started the final game before the All-Star break last Sunday against the New York Yankees.
