The rookie left-hander pitched eight shutout innings, helping Toronto complete a three-game sweep with a 1-0 victory over the Tampa Bay Rays on Sunday, and extending the Blue Jays' winning streak to eight games.
Jesse Carlson closed it out in the ninth for his second save and Toronto matched its longest winning streak since Apr. 14-22, 1999.
AL East-leading Tampa Bay lost for the fifth time in six games heading into a three-game series with second-place Boston that starts Monday night. The Rays have lost eight straight at Fenway Park.
"I think we might be putting a little bit of pressure on ourselves right now," outfielder B.J. Upton said. "We've just got to loosen up and go play our game, play the way we've been playing all year."
Garza (11-9), who allowed one run and six hits in seven innings, isn't troubled by the Rays' stumbling start to September, even though the Red Sox were just 2 1/2 games back entering play Sunday.
"We know what we've got to do and we know what they've got to do," Garza said. "Right now, we're up top and they're chasing us. If we can keep playing our ball, this thing will turn around. Right now we're in a little bit of a rut. It's nothing bad, we'll turn it around."
The Rays have never won a series in 25 tries at Fenway, losing 21 and splitting four.
"It's going to be a big crowd, big series," Upton said. "We just can't let it get to us."
Rod Barajas drove in the only run with a second-inning sacrifice fly for Toronto, which pulled within 9 1/2 games of the Rays. The Blue Jays started the day eight games behind the Red Sox in the wild card race.
Garza, who walked one and struck out seven, came in 3-1 with an 0.29 ERA in four starts against Toronto this season, and hadn't allowed a run in his past 24 1/3 innings against the Blue Jays. Two starts ago, on Aug. 27, he worked 7 2/3 shutout innings and Tampa Bay beat Purcey and the Blue Jays 1-0 on a solo homer by Carlos Pena.
"It's a give and take game," Garza said. "Last time I faced him I did the same thing."
Purcey (3-5) ended his outing by getting out of a jam in the eighth, loading the bases with two outs but getting Rocco Baldelli on a fly ball to left to end the inning.
"The best thing you can do is go right after somebody instead of trying to nibble too much, so that's what I tired to do," said Purcey, who allowed six hits, walked three and struck out seven.
"He kept us from stringing hits together," Upton said. "He did a great job of keeping us off the bases today."
Rays third baseman Willy Aybar hit a one-out single in the second but was thrown out at first by catcher Rod Barajas on a ball that bounced in the dirt. Jason Bartlett followed with a double, but Fernando Perez flied out to end the inning.
Utilityman Ben Zobrist, who was playing the outfield for only the 10th time this season, caught the ball in medium left but his throw was wide of the plate, allowing Lind to slide home safely.
It was Toronto's first run off Garza since May 7, when Marco Scutaro's RBI single broke a scoreless tie and chased Garza in a game the Blue Jays won 6-2.
Upton hit a leadoff single in the fourth but became the second Ray to be thrown out on the basepaths when Purcey picked him off first for the final out of the inning.
Upton said he was trying to time Purcey's move to the plate, but jumped a fraction too soon.
"We got to two outs and I was trying to make something happen, get into scoring position," Upton said. "I think I might have taken off just a little early. If I wait maybe another split second, he goes to the plate and I've got him."
Garza was left with seam marks on his arm after he was struck by Scutaro's liner with runners at first and second in the fifth. Garza recovered to throw out Scutaro on the play, then stranded runners at second and third by getting Alex Rios on a fly out.
"It hit me right on the meat part of the forearm," said Garza, who worked two more innings before coming out. "I was just thinking 'Don't tighten up, just get the out.' "
Rays 3B Evan Longoria took 60 swings before the game, 30 at an empty tee and 30 with a ball on the tee. Longoria, who was activated off the 15-day DL Saturday, hopes to take batting practice within the next couple of days. Rays C Dioner Navarro got the day off, and was replaced by Shawn Riggans. ... Tampa Bay's most recent win at Fenway Park was Sept. 10, 2007. ... Rios made his first career start at DH. ... The Blue Jays, who swept Minnesota last week, went undefeated on a homestand for the third time in franchise history.