Rios went 2-for-5 to raise his AL-leading batting average to .359. His 11th homer came off Britton (0-1) after Reed Johnson led off the seventh with a walk.
"It was a fastball. It was a big hit," Rios said. "We finished up winning, and that's good."
The homer came after a long foul ball that brought Orioles pitching coach Leo Mazzone out to the mound.
"It was almost the same pitch as the one I hit fair," Rios said.
Britton hadn't allowed a run since April 18, but he was pitching in a fourth straight game.
"He might have been a little tired. He probably needs a day off," Orioles manager Sam Perlozzo said. "But he's been throwing outstanding -- other than tonight."
Rios worked the count to 2-2 before driving a pitch into the left-field seats.
"You can't make a mistake up here or you'll pay for it. I found out the hard way tonight," said Britton, who had yielded a run in only 12 of his previous 13 appearances. "My arm is not tired. If it was, I would have told (Perlozzo)."
Kevin Millar hit an RBI single off Justin Speier to bring Baltimore to 5-4 in the bottom half, but Toronto added a run in the eighth when Gregg Zaun doubled and scored on sacrifice fly by pinch-hitter Lyle Overbay.
Former Oriole B.J. Ryan worked the ninth for his 14th save in 15 chances. Three of his saves have come in Baltimore, and he was booed lustily as he walked to the mound.
"It comes with the territory," the left-hander said. "It's their right. They bought tickets, they can say whatever they want."
But the star was Rios, who extended his hitting streak to eight games.
"He's not showing any signs of cooling off," Toronto manager John Gibbons said. "He's very confident right now. He's just putting the bat on the ball."
Baltimore's Corey Patterson had his run of successive games with a stolen base end at nine. It was the longest streak in the majors in 20 years.
The Blue Jays took a 3-2 lead in the sixth. After a double by Wells, a hit batter and a single by Bengie Molina loaded the bases, Hill drove in a run with a two-out infield hit. Orioles starter Erik Bedard avoided further damage and ended his stint by retiring Alfonzo on a grounder.
"I did all right," Bedard said. "I made some good pitches when I needed to, and some bad ones when I didn't need them."
The Orioles pulled even in the bottom half against reliever Scott Downs (1-0). With the bases loaded and one out, Nick Markakis hit a high chopper that Hill mishandled in an effort to get a double play.
The Blue Jays tied it in the second when Shea Hillenbrand hit a leadoff single and scored on a two-out single by Hill. An RBI single by Patterson made it 2-2 in the bottom half.
Taubenheim allowed two runs and five hits in five innings.
- Female golfer Michelle Wie threw out the ceremonial first pitch. The right-hander tossed a lob to bullpen coach Rick Dempsey that fluttered to the right of the strike zone. The 16-year-old Wie will compete in Maryland this week in the LPGA Championship.
- Baltimore's Brian Robertswent 0-for-5 and is mired in an 0-for-19 funk.