The victory could come at a price for the Blue Jays because Burnett left his start after four innings because of a sore right elbow.
Burnett, who signed a five-year, $55 million deal with the Blue Jays in the offseason after spending seven seasons with the Florida Marlins, began the season on the DL after scar tissue broke off in his elbow March 18 during spring training.
Blue Jays spokesman Jay Stenhouse said it was "consistent with what (Burnett) experienced in spring training." But Burnett will be examined by Dr. James Andrews in Birmingham, Ala.
The scar tissue is left over from elbow ligament replacement surgery three years ago.
"Something wasn't right," Burnett said. "It's pretty frustrating. I feel about two inches tall."
Burnett said he's willing to miss a month to make sure he's OK.
"I want to make sure it is out of there for good. Whatever it is, there is a shark floating in there and we got to get it out," Burnett said.
Toronto's Vernon Wells said Burnett should take his time getting healthy.
"Hopefully, it's not as bad as some people may think," said Wells, who homered twice off Boston starter Josh Beckett.
Down 6-2 in the eighth, Beckett plunked Aaron Hill with his first pitch of the inning, prompting a warning from plate umpire Jeff Kellogg.
"It was uncharacteristic. I was a little surprised by the warning," Red Sox manager Terry Francona said.
"It was definitely a pitch that got us going," Wells said. "It got everything going for us. It worked out well. Hill is going to have a pretty big bruise, but it got things started."
After Beckett nailed Hill, Russ Adams homered. One batter later, Wells chased Beckett with his second homer and cut the lead to 6-5.
Mike Timlin relieved and allowed a tying home to Glaus.
Keith Foulke (0-1) walked Glaus with two outs in the 12th before Rudy Seanez relieved and allowed Overbay's double to left center. Glaus chugged around the bases and slid headfirst for the winning run.
"Whether Beckett did it on purpose or not it got us going," Overbay said.
Justin Speier (1-0) pitched two innings for the victory.
Ramirez went 16 games without a homer -- the longest drought of his career to start a season. After David Ortiz homered in the third, Ramirez hit Burnett's next pitch for his first -- the ninth time they've hit back-to-back homers.
Ramirez added a two-run shot off Scott Schoeneweis in the seventh, giving Boston a 6-2 lead. Ramirez has 44 multihomer games in his career.
Beckett took a three-hitter into the eighth before, but allowed five runs on five hits in 7 1/3 innings.
Beckett denied hitting Hill on purpose.
"Anybody who was watching the game knows I didn't do it on purpose," Beckett said.
Wells said Beckett had pinpoint control before that.
Ortiz's two-run shot and Ramirez's solo shot gave Boston a 3-0 lead in the first. Both balls landed near each other in left center.
Wells cut it to 3-2 in the fourth with his first homer of the game.
Jason Varitek hit a solo shot for Boston in the sixth.
- Ramirez has 201 home runs with Boston, just the fourth player in team history to reach 200 homers.
- Ramirez has 49 career homers against Toronto -- the most by an opponent.
- Burnett threw 78 pitches. He threw 95 in his first start.
- Beckett has thrown seven innings in each of his four outings this season.
- Burnett allowed three runs on five hits in four innings against Boston. He lost his first start of the season, allowing four runs and seven hits in six innings of a 4-2 loss to Chicago on April 15.
- Wells has 11 multihomer games in his career. His last was April 7, versus Tampa Bay.