The right-hander allowed singles in the second, third and fifth innings to Allen Craig, Mookie Betts and Rusney Castillo, respectively. He also struck out four on 55 pitches before being lifted with two outs in the fifth.
"I want to go as deep as I can each and every game (and) put the boys in position to win," Stroman said. "I’m looking to go nine a lot this year, and anything I can to keep that efficiency up and to keep my pitch count low, I’m going to do."
Stroman, who is expected to fill the void atop Toronto’s rotation following the off-season departure of ace David Price, previously struck out four in his second start against Houston on Sunday.
He missed nearly six months last season recovering from a torn anterior cruciate ligament in his left knee before returning for four starts in late September, going 4-0 with a 1.67 ERA.
Thursday marked one year since Stroman sustained the injury during a fielding drill last spring training.
"Honestly, it was the biggest blessing in disguise I've ever had," he said. "I feel great. I can't put into words how strong I feel - my emotion, my pitches - and I'm just excited to get to opening day."
Boston prospect Sam Travis homered to centre field with two outs in the ninth.
Toronto prospect Jon Berti drove in the winning run in the 10th on a single to centre.
Red Sox: Steven Wright yielded three hits in four scoreless innings. The right-hander also walked one and struck out one on 55 pitches, 35 strikes.
Blue Jays: Manager John Gibbons stopped short of naming Stroman the starter for Toronto's opener at Tampa Bay on April 3, but hinted that an announcement is forthcoming.
"I'll let you guys (the media) look at the calendar and kind of add things up, and then we'll officially announce something in a few days, I'm sure," he said.
Red Sox: RHP Koji Uehara is scheduled to pitch in relief on Saturday against the Marlins. The former All-Star is returning from a broken right wrist he sustained in August that ended his season.
Blue Jays: 1B/DH Edwin Encarnacion, out since having an abscessed tooth pulled on Feb. 28, said he will take live batting practice on Sunday and Tuesday and should make his spring debut Wednesday against the Yankees in Tampa or Thursday against the Astros in Kissimmee.
Red Sox: Craig Kimbrel is scheduled to make his second appearance of the spring on Saturday against the Marlins in Fort Myers. The four-time All-Star closer, who was acquired in a November trade from San Diego, pitched a perfect fourth inning against the Rays on March 4.
Blue Jays: R.A. Dickey will make his third start Saturday against the Phillies in Clearwater. The 2012 NL Cy Young Award winner tossed three scoreless innings against the Braves on Monday