Relievers Wilton Lopez and Miguel Castro were equally stingy. The Jays (3-2) retired 18 straight batters (translating into 19 outs thanks to a double play) after veteran starter Mark Buehrle started the day by yielding two singles.
A Darin Ruff single off Steve Delabar in the seventh inning finally ended the Phillies' hitting drought before a sellout crowd of 8,759 on a breezy 20-degree afternoon at Bright House Field.
Josh Donaldson hit his first home run as a Blue Jay, a solo shot deep to left field. Caleb Gindl, Matt Hague and Kevin Pillar, with his fourth RBI of the spring, also drove in runs.
Outfielder Dayan Viciedo recorded his first hit as a Jay, a double in the right-field corner.
Philadelphia (1-3-1) finally got on the board with a pair of runs in the ninth. Toronto outhit the Phillies 10-6.
Buehrle found himself with men on first and third, with no outs in the first after back-to-back singles, the second of which caromed off the pitcher's foot. But a popout followed by a double play engineered by slick-fielding first baseman Daric Barton ended the threat.
Buehrle, who turns 36 later this month, disposed of the Phillies 1-2-3 on six pitches in the second inning.
"I couldn't have drawn it up any better," said Buehrle who has pitched more than 200 innings in each of the last 14 seasons. "I hit my spots where I wanted to, worked pretty much through everything out there.
"If you could tell me I would do this every time out there, I'll take it. I felt good."
The 31-year-old Estrada followed and put the Phillies down in order in each of his innings, using his 78 mile-per-hour change-up in tandem with a 90 m.p.h. fastball.
Estrada, who spent the last seven seasons with Milwaukee and Washington, said he is preparing as a starter with an off-season fitness regimen that included long-distance running and longer bullpen sessions.
"That way if I have to start, awesome, I'm prepared for it," he said. "And if I don't, it's an easier transition to go to the bullpen ... I'll just work as a starter for now and we'll see what happens."
Estrada is battling Aaron Sanchez and Daniel Norris for the fifth starter spot, although Sanchez may be withdrawn from the competition if the Jays decide he is needed at closer.
Castro, meanwhile, hit 97 m.p.h. on the speed gun in his one inning. Just 20, the six-foot-five Dominican flame-thrower has impressed so far this spring.
Kyle Drabek pitched out of trouble in the eighth, leaving two men on base, after Munenori Kawasaki dropped the ball at second trying to turn a double play.
Jayson Aquino gave up two Phillies hits to open the ninth before giving way to Ryan Tepera, who eventually cleaned up the mess.
Philadelphia starter Jerome Williams wore his trademark pink glove to honour his mother, who died of breast cancer in 2001. The veteran right-hander gave up one run on two hits in three innings with one hit batsman.
Follow @NeilMDavidson on Twitter