While John Lackey raised his record to 10-2 and Francisco Rodriguez recorded his 47th save, Aybar's play was the biggest in the victory.
With the Angels leading by a run, Oliver relieved Lackey to start the seventh and immediately loaded the bases with two walks and a single. He then struck out Kelly Shoppach on a 2-2 pitch.
Enter Aybar, who took over as the Angels' starting shortstop on Friday because of Maicer Izturis' season-ending thumb injury. Garko's blooper looked like a sure bet to fall into shallow left field, but Aybar got an excellent jump on the ball and made a backhand, leaping catch. He hung on to the ball after hitting the ground and got to his feet quickly before the runners could advance.
Oliver retired pinch-hitter Jamey Carroll on a tapper to the mound, ending the threat.
Aybar's play was a big topic of conversation in the Angels clubhouse.
"That's something you'll see on Web Gems," Oliver said. "I knew he was going to make that play."
Scioscia, from his vantage point in the dugout, wasn't so sure.
"Off the bat, I thought it was in there," he said. "He went a long way. That's as much range as you're going to see from a shortstop. That was incredible."
The deciding vote goes to Aybar and even he wasn't so sure.
"I didn't think I was going to catch it," he said, through translator Ervin Santana. "The way it came off the bat, I thought it would get out there quicker. I ran fast and made the catch."
Lackey (10-2) allowed three runs in six innings, raising his road mark to 6-1 while Rodriguez worked the ninth for the save, which tied the club record he set in 2006.
Lackey gave up a solo homer to David Dellucci in the first and a two-run blast to Garko in the third. Both were on 2-0 counts.
"I was only upset about the second one," Lackey said. "It was a dumb pitch. I should have thrown him a cutter. On the first one, it was the first inning. I wanted to go ahead and challenge him."
Scot Shields worked the eighth. Rodriguez gave up a single to Jhonny Peralta to lead off the ninth, but struck out Shin-Soo Choo. Peralta took second on Kelly Shoppach's groundout before Rodirguez struck out Garko on a 3-2 pitch.
The Angels did get some help offensively, thanks to shoddy defensive play by the Indians. Vladimir Guerrero had the Angels' only two RBIs of the game. Three Indians errors and two wild pitches by Fausto Carmona helped the Angels score four times in the first three innings.
Chone Figgins started the game with a single off Carmona. Peralta couldn't handle Mark Teixeria's one-out grounder for an error and the runners moved up on Carmona's first wild pitch. Guerrero's groundout made it 1-0.
After Aybar drew a one-out walk in the third, Teixeria singled to right. As Aybar slid in safely at third, the throw from right fielder Ben Francisco bounced into the camera bay. Aybar was awarded home and Teixeria went to third.
Third baseman Andy Marte threw wildly on Guerrero's ground ball. Guerrero ended up at second and was given an RBI as Teixeria scored.
With Torii Hunter batting, Guerrero stole third and continued home when Carmona's second wild pitch went to the backstop.
"We really didn't swing the bats very well," Scioscia said. "Fortunately, we created some offense."
Garret Anderson had two hits, extending his hitting streak to 20 games. He's batting .386 (32-for-83) during the streak.