"In a pitching sense, he was the bend but not break," Tampa Bay manager Joe Maddon said. "Wavered a bit in the beginning but he did not cave in, and that's a beautiful thing about him."
Moore (10-3) tied career highs with six walks and 11 strikeouts en route to his 10th win this season and second straight after a three-game skid. The left-hander gave up four hits.
"Any time where there's six walks and I can get through the sixth inning, it's a pretty unusual thing to happen," Moore said.
Tampa Bay rookie Wil Myers had an RBI single during a three-run fourth. Considered one of baseball's top prospects, the outfielder has eight RBIs in nine games since being called up June 18 from Triple-A Durham.
Mark Buehrle (4-5) gave up four runs, eight hits and four walks in five innings for the Blue Jays, who have lost two in a row since arriving at Tropicana Field after tying a franchise record with 11 consecutive wins.
Toronto, by dropping the first two games of the three-game set, has not won a series at Tampa Bay since April 2007, a stretch of 19 series.
The Blue Jays get their leadoff hitter back Wednesday when shortstop Jose Reyes, sidelined since mid-April by a left ankle injury, will be activated from the disabled list.
"I'm very excited about it," Reyes said. "I missed two months of doing what I love to do and now I know I'm going to be on the field one more time around my team. The way they're playing, I want to be part of the success they're having right now."
Blue Jays manager John Gibbons said Reyes has no limitations.
"He's one of those centerpieces of our team," Gibbons said. "Before he got hurt he was great. He was playing really well. He's been gone a while and now maybe he can put us over the top. We'll see."
Toronto loaded the bases with one out in the third, but failed to score when Moore struck out Rajai Davis and Colby Rasmus. Toronto entered hitting .194 this season with the bases loaded.
Jake McGee, Kyle Farnsworth and Jamey Wright completed the six-hitter.
Tampa Bay went ahead 4-1 in the fourth on consecutive sacrifice flies by Sean Rodriguez and Ben Zobrist, and an RBI single from Myers, who was part of a multiplayer offseason deal that sent pitchers James Shields and Wade Davis to Kansas City.
Toronto right fielder
Jose Bautista almost threw out slow-footed catcher Jose Molina on Rodriguez's fly.
"I was pretty much watching the incredible throw by Bautista," Maddon said. "He throws it right on the plate. How does he do that from that distance?"
After Zobrist hit his sac fly and
Evan Longoria was intentionally walked, Myers completed the three-run outburst with his hit.
Blue Jays reliever
Brett Cecil entered in the seventh and gave up a leadoff single to Yunel Escobar that ended his team-record streak of not allowing a hit over his previous 40 at-bats. Kelly Johnson made it 5-1 later in the inning with a run-scoring grounder.
Maicer Izturis put the Blue Jays up 1-0 with an RBI single in the second. The Rays tied it in the bottom half on
Desmond Jennings' run-scoring single.
NOTES: Tampa Bay LHP
David Price (left triceps) will make his second start for Class-A Charlotte on Wednesday night. "What it's going to tell us is what the next step's going to be, what we have to do," Rays manager Joe Maddon said. The AL Cy Young Award winner is scheduled to throw around 70 pitches. ... Toronto manager John Gibbons said there will be no limitations on SS Jose Reyes, who will be activated from the disabled list Wednesday after being out since mid-April due to a left ankle injury. ... Blue Jays 3B Brett Lawrie (left ankle) is expected to start a minor league rehab assignment Wednesday. ... Toronto RHP Sergio Santos (right triceps) threw off a bullpen mound.