Stroman (2-0) allowed two runs and three hits in eight innings to win his seventh consecutive decision.
"My curveball and slider were very good and so was my sinker," Stroman said. "I thought I was locating my sinker. I felt like I was down more than in my last game and the results showed."
They sure did. Stroman recorded 17 ground ball outs against four fly ball outs.
"He's a ground ball machine," appreciative manager John Gibbons said.
Stroman, who retired the final 11 batters he faced, improved to 5-1 with a 2.39 ERA in six career starts against the Yankees.
"He didn't give us many opportunities," Yankees manager Joe Girardi said.
Roberto Osuna finished for his fourth save as the Blue Jays salvaged a split on their six-game homestand after dropping three of the first four games.
Donaldson erased a 2-0 deficit with a second drive to center in the fifth. Tulowitzki snapped a 0-for-10 slump with a first-pitch blast in the sixth.
Both Toronto homers came off Nathan Eovaldi (0-1), who allowed four runs and seven hits in 6 2/3 innings. Donaldson is 3 for 10 with two home runs against Eovaldi.
"I've just got to do a better job of locating, especially my off-speed pitches earlier in counts," Eovaldi said.
New York broke a scoreless tie with two runs in the fourth. Carlos Beltran beat out a double play to drive in the first while the second scored on Stroman's wild pitch.
Alex Rodriguez said he was frustrated the Yankees couldn't do more after putting Stroman "on the ropes" in the fourth.
"We felt like we let one get away," he said.
New York has lost 20 of its past 31 meetings with Toronto.
Rodriguez went 1 for 3, dropping his average to .120. He went 1 for 15 on New York's five-game road trip.
"I felt great today at the plate," Rodriguez said. "I thought I had good swings, I swung at strikes, had my `A' swing. I didn't like the results, but tomorrow is another day."
Donaldson's two-out homer in the fifth gave the reigning AL MVP at least one hit in all 10 games this season.
"That's why they call him the MVP," Gibbons said.
Tulowitzki gave the Blue Jays an insurance run with his homer, the 40th time in his career he's connected on the first pitch.
Toronto's Kevin Pillar singled on a ball that bounced off second base in the first, then doubled on a ball that bounced off third base in the fifth.
CATCH OF THE DAY
Yankees left fielder Brett Gardner made the defensive play of the game, leaping backward into the first row of seats to catch Ryan Goins' foul popup in the third. Gardner also made a sliding catch on Bautista's sinking liner to end the fifth.
SWISHER MAKES TRIPLE-A DEBUT
After signing a minor league contract with New York, INF/OF Nick Swisher started at 1B in his debut for Triple-A Scranton/Wilkes Barre. He finished 1 for 4 with a single.
Yankees: C Brian McCann returned to the starting lineup two days after leaving with a bruised big left toe. He went 1 for 4 with a single and struck out once.
Yankees: New York returns home Friday to begin a three-game series against Seattle. RHP Luis Severino (1-0) faces RHP Nathan Karns (0-1) in the opener. Severino has never pitched against the Mariners.
Blue Jays: Toronto begins a four-game series at Boston on Friday. RHP R.A. Dickey (1-1) starts against Red Sox RHP Rick Porcello, who beat Dickey and the Blue Jays in his season debut last Saturday. Dickey has a 3.99 ERA in 10 career games at Fenway Park.
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