"He's been better than advertised," Blue Jays manager John Gibbons said. "That's his third two-homer game. Not only that, but he's a leader. You can't overlook his glove, too. He's made some big plays."
Glaus hit a three-run homer off Kirk Saarloos (1-1) in the third inning and a solo shot in the fifth for his 21st career multihomer game.
Glaus waived a no-trade clause to come to Canada, and he's hitting .274 with 12 home runs and 30 RBI.
"I'm having a good time. There is a great group of guys in here and we are starting to put some things together," Glaus said. "We'd like to kick it up a notch and win six or seven in a row."
Gregg Zaun also homered for the new-look Blue Jays (19-15), who moved four games over .500 for the first time this season.
Lilly (4-2) allowed three runs and five hits in 7 2/3 innings. He struck out two and walked four.
"We haven't gone on a big wining streak, but to our credit we've played some consistent baseball," Lilly said.
Nick Swisher homered twice for the A's.
Swisher hit solo shots in the first and third for his third multihomer game this season and the fifth of his career. He is 5-for-11 lifetime against Lilly.
"We feel we should be doing a lot better, but that's kind of how the cookie crumbles," said Swisher, whose team is 17-16 despite some injury woes.
Glaus' three-run homer gave Toronto 4-2 lead in the third.
Frank Catalanotto followed with a sacrifice fly to make it 7-2.
Glaus made it 8-2 in the fifth with his solo shot.
Saarloos allowed eight runs -- six earned -- in five innings in his second start of the season. After nine appearances out of the bullpen, Saarloos won his first start last Thursday against Cleveland.
"I'm sure he feels he could have been better," Oakland manager Ken Macha said. "He made some mistakes to Glaus. He left balls up. But he gave me all he had today."
- An MRI revealed Toronto left-hander Gustavo Chacin has a mildly sprained ligament in his elbow and a strained forearm. He is day to day. Chacin left his start on Wednesday after just three innings. "We'll see how it feels after I play catch," Chacin said. He said he would take a couple of days off before playing catch.
- Gibbons gave center fielder Vernon Wells his first day off this season. Johnson played center in his place. Johnson robbed Scutaro of a hit with a leaping grab at the wall in the seventh. Alex Rios hit third in Wells' place.
- Oakland third baseman Eric Chavez missed his third straight game due to illness.
- Toronto begins a nine-game road trip on Friday, with series against Tampa Bay, the Los Angeles Angels and Colorado.
- Glaus last hit two home runs May 1 at Baltimore.