Boston, which tied the best-of-seven series at two, was outshot by Vancouver, 37-29, and both teams had four power play opportunities, but neither could convert. The Bruins have now outscored the Canucks 12-1 in the last two games.
Tim Thomas recorded yet another shutout, turning away all 37 shots he faced. Roberto Luongo struggled once again, giving up four goals on 20 shots (16 saves), and was pulled in the third period. Boston College graduate Corey Schneider entered for Luongo and turned away all nine shots he faced.
Peverley scored the game's first goal 11:59 into the first period, assisted by David Krejci and Zdeno Chara.
The Bruins tacked on two goals in the second period, with Michael Ryder scoring his seventh goal of the postseason at the 11:11 mark in the second period (assists from Tyler Seguin, Chris Kelly). Brad Marchand put the Bruins up 3-0 with his eighth goal of the playoffs 13:29 into the period, assisted by Patrice Bergeron.
Peverley netted his second and final goal 3:39 into the third period, sealing the victory.
Boston travels to Vancouver for Game 5, which takes place at Rogers Arena on Friday night at 8 p.m. EDT.