TORONTO -- There's no way Shelby Miller could have predicted how his day was going to unfold after the way it started.

The St. Louis Cardinals right-hander said he didn't feel good warming up, but ended up disposing of the Toronto Blue Jays in dominating fashion, using 105 pitches to record 27 outs and blank the hottest team in baseball.

Miller threw the second complete game of his career and Randal Grichuk hit his first career home run to power the Cardinals to a 5-0 victory over the Blue Jays at Rogers Centre.

"It's crazy how the game works," Miller said. "I'm a little speechless still. It was a lot of fun doing that."

Miller (7-5) flirted with perfection and lost his no-hit bid in the sixth but settled for a three-hit shutout to snap Toronto's six-game winning streak.

The 23-year-old bounced back from three rough outings in which he allowed 15 runs over three losses to record his first shutout since one-hitting the Colorado Rockies last May.

Miller, who logged his fifth quality start of the season, walked one and struck out six to send the Cardinals to their third victory in their last 11 games.

Blue Jays manager John Gibbons singled out Miller's fastball as the difference, a pitch that was routinely hitting 95-plus mph and generating swings and misses.

"He carved us up pretty good," Gibbons said.

Grichuk's solo blast to dead-center field off Mark Buehrle in the fifth inning broke open a scoreless game and put the Cardinals (32-31) ahead, 1-0, giving Miller all the run support he needed on the sunny afternoon.

"He hammered that ball," Cardinals manager Mike Matheny said. "Not many guys have that kind of juice to the center of the field."

Buehrle said the home run came on an outside changeup he left a little up in the zone.

"If it was down a few more inches, it probably would have been better off," Buehrle said. "But just tip your hat to him."

Grichuk's solo shot was the only run Buehrle (10-2) surrendered despite issuing a season-high-tying five walks. The left-hander lasted seven innings, allowed five hits and punched out six.

Buehrle allowed one earned run or fewer for the seventh time this season and recorded his eight consecutive quality start in his first loss since April 25.

The Cardinals added four runs in the eighth inning off relievers Aaron Loup and Steve Delabar to silence the crowd of 42,981. Loup and Delabar each issued bases-loaded walks and catcher Tony Cruz provided the rest of the damage with a two-run single.

Miller mowed through the Blue Jays (38-25), retiring the first 13 batters before issuing a one-out walk to first baseman Adam Lind in the fifth inning.

Toronto was unable to capitalize, however, as Miller's defense came up with two strong plays in a row to end the inning.

First baseman Allen Craig reached to his right to snare a chopper off the bat of second baseman Brett Lawrie and Miller ran to the bag to take the throw to get the second out of the inning on a bang-bang play.

Peter Bourjos then reeled in the final out of the inning, jumping into the wall in center to catch a long fly ball hit by designated hitter Juan Francisco.

Shortstop Jose Reyes snapped Miller's no-hit bid in the sixth with a two-out single to right field. Left fielder Melky Cabrera promptly followed with a double on a grounder that went off the glove of a diving Craig and trickled into right-center field to put runners at second and third for Jose Bautista.

But Miller buckled down, and blew a 97-mph fastball up in the zone past Bautista to retire the Blue Jays right fielder on strikes.

"He turned it up, no question," Cardinals manager Mike Matheny said about the pitch. "That's a huge part of the game right there, obviously, with one of the best hitters you're going to see."

Toronto, shut out for the second time this season, did not get a better opportunity after that, as Miller went on to allow one baserunner over his final three innings.

NOTES: Cardinals 2B Kolten Wong (left shoulder) sat out for the second consecutive game and is considered day-to-day. ... St. Louis C Yadier Molina got the day off Saturday. Manager Mike Matheny said his star catcher is physically fine and the rest is simply a mental break. ... Blue Jays RF Jose Bautista had a 12-game hitting streak snapped. ... Toronto RHP Drew Hutchison will get the ball for Sunday's series finale against Cardinals LHP Jaime Garcia.