Melky Cabrera had three hits and three RBIs as the AL East-leading Blue Jays won for the 12th time in 14 games.
Hutchison struggled through five innings but won his career-best third straight start thanks to a lineup that had 16 hits, with all nine starters picking up at least one.
"I didn't have to do too much because of what they were able to do," Hutchison said.
Toronto has hit at least one home run in nine straight games and leads the majors with 73 this season, including an ML-best 41 in May.
"They just put the heavy gloves on and beat us up tonight," Rays manager Joe Maddon said.
Hutchison (4-3) allowed five runs and seven hits, matched a season-worst with four walks and struck out none.
"I wasn't locating my fastball very good at all," Hutchison said. "Nothing was good, nothing was sharp."
Catcher Dioner Navarro said he knew early that Hutchison didn't have it.
"It was a battle," Navarro said. "I sensed that early in the game, I kind of knew it was going to be one of those days."
It was one of those days, too, for Rays starter Erik Bedard, as Toronto jumped on the left-hander with five straight hits to start the first.
Encarnacion and Brett Lawrie both singled, but Bedard got Navarro and Tolleson to fly out.
"They're hitting every hole," Bedard said. "Everything was going their way. They hit good pitches and everything."
The Rays tied it in the third on a homer by DeJesus and a sacrifice fly by Loney, but the Blue Jays reclaimed the lead with three in the third.
Navarro and Tolleson opened the inning with home runs on consecutive pitches from Bedard, who'd only allowed one home run in 37 2/3 innings coming into the game.
It was the third time this season the Blue Jays have gone back-to-back. Cabrera made it 5-2 with a two-out RBI single.
Tampa Bay battled back to tie it at 5 with a three-run fifth. Matt Joyce doubled and scored when Jennings homered on the first pitch. Loney followed with a blast to right, the first time this season the Rays have hit consecutive homers.
"It was just not enough," Maddon said. "They kept adding on."
Toronto answered with a four-run, bat-around inning in the bottom half. Lawrie hit an RBI double and scored on Navarro's ground ball single, which chased Bedard. Alex Colome came on and issued a bases-loaded walk to Reyes, then gave up a sacrifice fly to Cabrera.
Bedard (2-3) lost his second straight start, allowing eight runs in four innings. He walked none, struck out two and had his ERA rise from 2.63 to 4.10.
Encarnacion led off the sixth with a booming drive to left off Colome, his 15th homer of the season. The 13 home runs this month are a Blue Jays record for May, breaking the mark set by Bautista in 2010. Toronto's team record for home runs in a single month is 14, set by Bautista in June 2012.
The Rays placed OF Brandon Guyer (left thumb) on the 15-day DL and recalled Colome from Triple-A Durham. Colome, who reinstated Sunday after being suspended 50 games in March for a drug violation, was sent back down following the game. The Rays will promote a position player Tuesday. ... Both teams wore special caps and jerseys to mark the Memorial Day holiday. The umpires also wore commemorative caps. ... Rays RH Alex Cobb (1-1) faces Blue Jays LH Mark Buehrle (8-1) on Tuesday.