Catcher Jose Lobaton, batting ninth, led the offensive effort, going 2-for-4 with three RBIs, while Evan Longoria went 3-for-5 with two RBIs.
"When I'm at home plate, I'm trying to do the best for the team," Lobaton said. "Thank God I got that blooper in the [second inning] that kept us in the game. And in the other at bat, I just tried to do the same and got a good result."
Sam Fuld, the leadoff hitter, was the only player not to record a hit, but he reached base on a walk in the second inning.
The six runs scored by the Rays were the most in their last nine home games.
"We found some holes, put some balls in play, we moved the ball," Maddon said. "I do like the idea that we're getting base hits and working better at-bats, period. If we do do that, it'll turn out a lot better for us."
Meanwhile, Tampa Bay's pitching, which entered the game with a Major League-best 2.27 ERA since the All-Star break, continued to dominate. Starter Matt Moore allowed a single run over six innings on two hits and two walks to go along with six strikeouts.
The young lefty's day got off to a rough start, however, as he surrendered a leadoff double to Rajai Davis. After a Colby Rasmus strikeout, Moore walked Edwin Encarnacion. Davis scored the first run after Moore committed a balk, ending his streak of scoreless innings at 18.
"[The start] set up a pretty difficult road to get later into the game," Moore said. "I just didn't quite have the feel for things right there in the first inning."
The Rays gave Moore his first bit of run support in the bottom of the second with the bases loaded and one out when Lobaton singled in Ben Zobrist and Jeff Keppinger. Fuld walked to load the bases again, and B.J. Upton grounded in a run-scoring fielder's choice to make it 3-1.
"Today, [starter Henderson Alvarez] missed with location inside the strike zone a number of times and contributed with a couple of walks," Jays manager John Farrell said. "In the end, the three-run inning loomed large."
Zobrist scored again in the next inning when Ryan Roberts knocked a soft single to short center field with the bases loaded that Rasmus couldn't quite get to. Tampa Bay couldn't add any more runs, though, as Lobaton grounded into a double play to end the frame.
Longoria added to the Rays' lead when he singled in Upton with two outs in the bottom of the fourth, giving him his second RBI since coming off the disabled list. He then stroked an RBI double in the eighth that went off the top of the wall in left-center field. After a review, the play was upheld.
"The at-bats are better," Maddon said of Longoria, who had gone 1-for-7 with four strikeouts the previous two games. "The big thing for him is not to expand the strike zone. But when he's able to recognize a breaking ball and spin, heads up."
Maddon said after the game that Longoria's status is uncertain for Friday.
"We're gonna wait until I see how he feels [Friday], I'll talk to the trainers," Maddon said. "The point is to not break him."
The day belonged to Moore, however. After giving up a leadoff single in the second inning, the southpaw retired 14 straight Jays until walking Encarnacion in the top of the sixth with two outs.
"It just didn't start out well, but he settled in," Maddon said. "He started throwing some good curveballs, some good changeups, fastball picked up but started throwing strikes with it. That's what I want to see is strikes with the fastball."