Bolland, who had been sidelined with a concussion and was playing in his first game since March 9, scored an unassisted tally during the second period, when Chicago scored four unanswered goals.
The defending NHL champs scored twice in the final period for six straight goals, making sure there would be a Game 5 in their Western Conference semifinal series after losing three straight to the Canucks.
Patrick Sharp scored twice and Michael Frolik added a goal and two assists for Chicago.
Corey Crawford turned aside 21-of-23 shots in the victory, which turned into a slugfest in the final period when nine minor penalties, two 5-minute majors and six 10-minute misconduct penalties were issued.
Canucks goalie Roberto Luongo was pulled in the third period after allowing six goals on 28 shots. Cory Schneider entered and yielded one goal on seven shots the rest of the way.
Sami Salo and Daniel Sedin scored Vancouver's goals.