Guillen tapped Wise to enter the game in center field, moving Scott Podsednik to left in place of Carlos Quentin, before Buehrle took the mound in the ninth. Gabe Kapler led off the inning for the Rays and smoked Buehrle's 2-2 pitch to deep center field.
Wise sprinted for the fence, leapt, and made a spectacular catch in the air to rob Kapler of a home run that would have dashed Buehrle's bid for perfection.
Buehrle proceeded to get the next two outs, and the rest is history. In Wise's own words, it was the best catch of his career. And the most important.
"By far," Wise said. "Under the circumstances, a perfect game on the line, it's the best catch I ever made.
"Everything was going quick. It was like I caught the ball and hit the wall at the same time. I couldn't really feel it going into my glove, so I thought it was falling. I saw it slowly rolling out of my glove, and that's when I stuck my left hand out there and caught it."
Wise positioned himself at normal depth, not wanting to let a bloop single spoil Buehrle's perfect game.
"It was like everything was slow motion," Wise said. "I stuck my hand out so slowly and was able to make the catch."
Guillen didn't want to take credit for making the defensive switch, but was sure glad the struggling Wise was able to contribute something so meaningful to the team.
"That's our job," Guillen said of making the switch. "The last couple of nights, we never did it because I think we needed Quentin's bat just in case something happened. I asked [bench coach Joey Cora] about it and he said, 'I want to have some more range in the outfield.' That's what we needed to have.
"At least I got the monkey off my back. This kid did something good for the organization. Now people can smile about it. We kept him for a reason. He just makes the nice play and I think it is one of the best plays I've seen, especially in that situation."
No team wants to be no-hit, and Wise's catch all but sealed the deal. But the Rays gave credit where it was due.
"As a defensive player, you think about doing something like that for your teammates," Kapler, who coincidentally made two diving catches earlier in the game, said of the catch. "And there's not a more overwhelming, positive experience than doing something like that. You visualize something like that. That's the only way you make a play like he made, by seeing it happen before it happens."
"He might wake up tomorrow with a new car in his driveway," Rays designated hitter Pat Burrell added.
For Wise, it was his second perfect game -- but his first on the winning side.
"I was with the Braves in '04 and I was there when Randy Johnson of the Diamondbacks pitched a perfect game," he said. "So I've been on both sides of it. It was probably the best catch I've ever made because of the circumstances."