Price (10-4) allowed three hits, two walks and one run and struck out 11 in eight innings in his first start since he was obtained from the Detroit Tigers on Thursday.
With third baseman Josh Donaldson hitting a two-run homer and second baseman Ryan Goins belting a solo shot, the Blue Jays defeated the Minnesota Twins 5-1.
Right fielder Torii Hunter homered for the Twins (54-51).
Price was impressed as well by his welcome to Toronto by a sellout crowd. He was cheered during his warmups and the game and received a standing ovation as he left after the eighth inning -- he tipped his cap in return.
"That was the best atmosphere I've ever been in," Price said. "I've pitched in really big games: Game 163 in Texas to go to the playoffs, in Fenway it's an amazing atmosphere always, at the Trop in 2008 when we were in the playoffs with the cowbells and the dome that was really loud.
"Baltimore last year with Detroit, that was insane. And then Comerica as well. I've pitched in quite a few big games, but that atmosphere today, that takes the cake. I've never experienced anything like that. That was cool."
"That blows me away," Price said. "That's probably the coolest thing I've had happen to me fan-wise for somebody like that."
It was the first win for Price since July 9. He had been 0-2 with a no-decision in his final three starts with the Tigers.
The strikeouts were the most in a Blue Jays debut, surpassing the nine by right-hander Roger Clemens on April 2, 997.
Right-hander LaTroy Hawkins pitched the ninth.
Twins right-hander Ervin Santana (2-2) allowed six hits, three walks and three runs while striking out two in six innings.
"I didn't have good bite on my slider today," Santana said. "The changeup was very good; the two-seamer was good. One of those days.
"It was a like a playoff game today. It was very crowded, everybody was loud. I just got the adrenalin going. It was good. (Price) pitched like an ace today."
"There's different classes of pitchers in the league," Blue Jays manager John Gibbons said. "Anybody that's a starting pitcher in the big leagues is good. And then there's guys that kind of separate themselves. David's at the top. He's one of those guys. That's what they do."
Each team homered in the second. Hunter hit his 17th of the season, and Goins hit his third.
"I'm always surprised when I hit a homer," Goins said.
Price worked out of a bases-loaded jam with none out in the fourth after first baseman Trevor Plouffe had doubled and designated hitter Miguel Sano and Hunter had walked. Left fielder Eddie Rosario popped out to shortstop Tory Tulowitzki who made a fine play in shallow center field and made a quick throw home. Twins center fielder Aaron Hicks and catcher Kurt Suzuki struck out.
"We didn't get much going after that," Twins manager Paul Molitor said. "It was kind of tough. A game like today, when you have chances, you'd like to see guys take advantage of it. Next time hopefully they're better for it and more prepared to try and get something done."
"(Price) gets out of that unscathed," Gibbons said. "A lot of guys cave after that. It takes so much out of you to finish an inning, and then it gets tougher the rest of the game and they don't last eight innings anyway. That's kind of a telltale sign right there. I think he really enjoyed it; (he's) a very focused guy. Great way for you to make your debut for your new team."
Tulowitzki led off the fifth with a single and Donaldson followed with his 27th homer of the season -- a drive to right -- as the Blue Jays took a 3-1 lead.
The Blue Jays (55-52) added two runs in the seventh against right-hander Blaine Boyer, who replaced Santana.
Tulowitzki opened with a walk, took second on Donaldson's groundout and scored on a single by designated hitter Edwin Encarnacion, who took second on the throw home. First baseman Justin Smoak followed with an RBI single.
NOTES: Twins manager Paul Molitor played for the last Blue Jays team to reach the postseason, the 1993 World Series winners. Molitor batted .315 with 51 homers and 246 RBIs for the Blue Jays from 1993 to 1995. ... The Twins completed a 3-6 homestand before embarking on a seven-game trip that started Monday with the opener of the four-game series in Toronto. ... RHP Roberto Osuna, the Blue Jays' closer, earned his seventh save of the season Sunday by pitching 1 1/3 innings, his fourth save of more than one inning this season. The last Toronto pitcher to have four saves in a season of more than one inning was RHP Casey Janssen in 2007. ... Twins RHP Phil Hughes (10-6, 4.11 ERA) will start Tuesday against Blue Jays RHP Marco Estrada (8-6, 3.53). ... INF/OF Danny Valencia was claimed off waivers by the Oakland Athletics Monday. Toronto designated him for assignment on Friday.