Stewart allowed four hits and struck out four over six innings as Triple-A Pawtucket blanked Charlotte, 2-0, to take Game 2 of the best-of-5 Governors' Cup Finals on Wednesday.
The 25-year-old right-hander threw 58 of his 87 pitches for strikes and faced one over the minimum as he cruised to his second win of the International League playoffs.
"Couldn't ask for anything more," manager Arnie Beyeler told the Providence Journal.
"He was unbelievable," said catcher Dan Butler. "His slider and changeup really kept him in the game. Those guys didn't see too many good pitches to hit."
Stewart was acquired from the Chicago White Sox by Boston on June 24 in the Kevin Youkilis trade. He had spent the previous year as a member of the White Sox organization and had thrown one game for Charlotte in 2011.
Pawtucket needs to win one of the next three games in Charlotte to earn its first championship since 1984.
Pedro Beato tossed 1 1/3 hitless innings of relief, Alex Wilson recorded the final two outs of the eighth inning and Jose De La Torre pitched a perfect ninth for his third save of the playoffs.
"It's been somebody every time," Butler said. "Guys are just finding ways to scratch one together. It's always somebody new every day, and it's mostly because our pitchers are keeping us in games."
Butler was 2-for-3 with a homer and two runs scored and Che-Hsuan Lin smacked an RBI double for the Red Sox.
Charles Shirek took the loss after allowing two runs on six hits with six strikeouts over seven innings for the Knights.