"Watching them pitch now is a lot different," Halladay said of the first-place Rays. "They've always had good hitters, they've always made you work, but usually we got to their pitching. That's probably the biggest difference."
Halladay (12-8) lost 6-4 to Garza and the Rays at Tampa Bay on July 19, and dropped a 5-3 decision at Tropicana Field on April 23.
"When you face Halladay, you're not going to beat him up ever, so you have to pitch well," Rays manager Joe Maddon said. "That's been the mantra and we've got to keep doing that."
The only other team to beat Halladay three times in a season was the Boston Red Sox, who took three of four from the right-hander in 2007.
Halladay allowed three runs and six hits in eight innings. He walked three and struck out eight.
Garza (9-6), who benefited from three double plays, struck out five and walked one.
"I was able to find a rhythm early and get a lot of quick outs," Garza said.
The only extra-base hit against Garza was Adam Lind's two-out double in the eighth, but Brad Wilkerson ended the inning by grounding back to the mound.
"I told (Garza) after the game how hard it is to beat Halladay at home," Hinske said. "We only scored him one run for the first seven innings and he just kept shutting them down and shutting them down. It was huge for us."
Garza was acquired by Tampa Bay in an offseason trade with Minnesota. He pitched parts of the last two seasons with the Twins.
Hinske led off the third with a drive that cleared the center-field wall but ricocheted off the concrete facing of the lower deck and back into the outfield. Second-base umpire Mike Winters signaled no catch, but neither center fielder Alex Rios nor Wilkerson in right chased after the ball.
Hinske trotted around the bases while Halladay waved his arms and yelled until second baseman Joe Inglett ran out and threw home, too late to get Hinske, who sped around third and scored standing up for his 15th homer of the season.
"I kept going because the second-base umpire was ruling it safe," Hinske said. "I thought I saw it hit the facade over the fence and Rios and Wilkerson just stopped, but I wanted to make sure so I kept running."
The Rays got a laugh out of Hinske's antics on the basepaths.
"That was the fastest home run trot I've seen," Garza said. "I was like 'Man, slow down!'"
The home run sprint left Hinske out of breath by the time he got back to the dugout.
"I was gassed," he said. "I've never had an inside-the-park home run, I've never even attempted one. I got to third and (third-base coach Tom) Foley was waving me, 'Go, go,' so I gave it whatever I had left."
Originally scored an inside-the-park home run, the ruling was changed after the official scorer checked with the umpires and learned that first-base umpire Hunter Wendelstedt had ruled the ball cleared the fence.
B.J. Upton drew a two-out walk in the eighth and went to second on Carl Crawford's single before both runners scored when Longoria tripled off the wall in right-center.
Longoria made two great defensive plays, ranging into foul territory and throwing out Rios in the seventh and Matt Stairs in the eighth.
"He doesn't surprise me," Maddon said. "I think he's going to get better. I don't think you've seen anywhere near what he's going to look like eventually."
- Garza's strikeouts all came in a run of six batters during the fifth and sixth innings.
- The Blue Jays were shut out for the fourth time this season.
- Tampa Bay OF Rocco Baldelli (fatigue) was scheduled to be the DH Tuesday and Wednesday at Double-A Montgomery, then take Thursday off before playing the outfield Friday. Maddon said Baldelli could return "relatively soon" if he suffers no setbacks. "He's been responding well," Maddon said.
- Upset at losing playing time to Rod Barajas, Toronto C Gregg Zaun said he would welcome a trade before Thursday's deadline.