Pawtucket scored twice in the eighth inning to beat Durham 2-1 in the opening game of the International League championship series Tuesday.
Game 2 is Wednesday.
After starter Jake Odorizzi tossed seven shutout innings, reliever Jeff Beliveau gave up two runs on two hits and recorded just one out.
The Red Sox totaled just four hits, a walk and seven strikeouts against Odorizzi, who has thrown 14 shutout innings in the playoffs.
The Bulls loaded the bases with one out in the bottom of the ninth.
Tim Beckham singled and went to third on a Cole Figueroa single. Figueroa moved up to second on the play before the Red Sox intentionally walked Jason Bourgeois.
Shelley Duncan fouled out and Brandon Guyer flied out to end it.
The Bulls scored in the second inning. Mike Fontenot hit a leadoff double, went to third on a Kevin Kiermaier bunt and scored on a Jesus Flores flyout.
Beckham singled twice and walked. Figueroa hit two singles and Vince Belnome walked twice.