Shields threw eight strong innings, Evan Longoria drove in a run in his return from an injury, and the Tampa Bay Rays beat the Blue Jays 4-1 on Tuesday night.
Happ (0-1), making his first start with the Blue Jays, gave up four runs and seven hits in 4 1-3 innings. He had made four relief appearances since being acquired from Houston on July 20.
"The result is the only thing that matters, but I did feel better than, probably, the numbers indicate," Happ said. "I felt like I was making some good pitches. They used the whole field and they were falling for them, and weren't falling for us. A frustrating one for sure."
Happ's previous start, while with the Astros, came on July 16. The left-hander threw 6 1-3 innings in a 2-0 win over San Diego.
"I got upwards of 80 pitches in, and hopefully we'll keep moving from there," Happ said.
Happ had five strikeouts and one walk.
"They didn't square up too many balls," Blue Jays manager John Farrell said. "First time out, we're not going to jump to any conclusions or judgments, certainly. This is an established major league pitcher."
Blue Jays rookie Chad Jenkins, who had his contract purchased from Double-A New Hampshire on Sunday, worked three shutout innings in his major league debut.
"He came in and threw the ball over the plate," Farrell said. "Had good sink to his fastballs. Showed a good slider as well. And didn't show any fear of contact. It was encouraging to see that kind of aggressiveness out of him."
Colby Rasmus hit his 20th homer, a solo shot in the fourth, that got Toronto within 3-1. Rasmus, who had missed the previous two games because of tightness in his right groin, singled in the ninth.
Shields (10-7) allowed one run and two hits. The right-hander was coming off a three-hit shutout last Tuesday at Oakland.
"Shields really held us down," Farrell said.
Longoria rejoined the Rays after missing 85 games because of a partially torn left hamstring. He went 1-for-3 with a sacrifice fly as the designated hitter.
Fernando Rodney pitched the ninth for his 33rd save and completed the three-hitter.
Longoria got a standing ovation before his first at-bat in the second, when Happ reached behind his legs to glove a grounder and then threw out the three-time All-Star.
Longoria made it 2-0 on a bases-loaded sacrifice fly in the third, an opposite-field drive caught at the wall by right fielder Moises Sierra. Jeff Keppinger extended the lead to 3-0 on another sacrifice fly later in the inning.
The Rays stopped a 22-inning scoreless stretch and took a 1-0 lead in the second as Ryan Roberts hit a two-out pop fly double down the right-field line and scored on Sean Rodriguez's single.
Tampa Bay went ahead 4-1 in the fifth on Ben Zobrist's RBI double.
Notes: Farrell said OF Jose Bautista, out since July 17 with left wrist inflammation, still has some soreness on a small area of the hand and will undergo an MRI. ... Blue Jays INF Brett Lawrie missed his third straight game due to rib cage tightness. ... Toronto RHPs Drew Hutchison and Dustin McGowan are both scheduled to have surgery Thursday. Hutchison will have elbow ligament surgery, while McGowan is scheduled for arthroscopic surgery to evaluate the right shoulder joint. ... Blue Jays 3B Adeiny Hechavarria singled in the third for his first major league hit.