Correia came in 1-4 in his past six starts, and 1/3 with a 7.04 ERA in four career starts against Toronto, but settled down after allowing four hits in the first two innings. The right-hander got Melky Cabrera to ground out to end the second, leaving the bases loaded, starting a stretch of 12 consecutive outs.
"It looked like he was kind of searching to find it," Gardenhire said, "but once it got going he got his confidence, started making pitches. Great performance by him."
Toronto used two singles and a walk to load the bases with one out in the second, but Correia snared Reyes' grounder, throwing home for the second out, before retiring Cabrera to keep the Blue Jays scoreless.
"Outstanding, wasn't it?" catcher Kurt Suzuki said of the backhanded snag. "That was pretty cool. That was a big play for us. Big play."
Correia left after Dioner Navarro's leadoff single in the seventh. After Brian Duensing got two outs, Reyes singled to put runners at first and second, but Duensing escaped when Cabrera lined out to third.
Happ (5-3) lost for the second time in three starts, allowing four runs, three earned, and six hits in 3 2/3 innings. He walked three and struck out three.
"He was getting ahead but he just couldn't put anybody away," Blue Jays manager John Gibbons said. "He had to work way too hard tonight."
Minnesota RH Mike Pelfrey underwent surgery Tuesday to relieve a nerve problem in his surgically repaired elbow and will miss at least two months. Pelfrey, who had ligament replace surgery in 2012, has been on the DL since May 2 with a strained left groin. ... Blue Jays RH Sergio Santos (elbow) allowed three runs in one inning in his first rehab appearance at Double-A New Hampshire. ... Twins 3B Trevor Plouffe got the day off, only the second time this season he has not played. Nunez started at third. ... Twins OF Sam Fuld (concussion) went 1 for 3 in a rehab game at Double-A New Britain, hitting a leadoff home run in the first. ... Minnesota OF Aaron Hicks (right shoulder) is still sore and could be sent home for tests if his condition does not improve. ... Twins RH Phil Hughes (6-2) faces Blue Jays RH Marcus Stroman (2-0) in Wednesday's series finale, a 12:37 ET start.
Copyright by STATS LLC and The Associated Press
TORONTO, ON - JUNE 10: J.A. Happ #48 of the Toronto Blue Jays throws a pitch against the Minnesota Twins in the...
B Dozier homered to left (376 feet), D Santana scored.
D Santana reached on infield single to third, K Morales scored, O Arcia to third, E Nunez to second, O Arcia scored, E Nunez to third, D Santana to second on throwing error by third baseman J Francisco.