After a scrambled faceoff to the right of Calgary goaltender Miikka Kiprusoff, the puck squirted to Bulis alone in the slot and he knocked a quick wrist shot over Kiprusoff's glove.
Ryan Kesler and Josh Green scored 51 seconds apart midway through the first period for a Vancouver team (2-5-0) that dressed all its regulars except defenseman Lukas Krajicek, who missed the game with the flu.
Jarome Iginla converted a power play just 1:46 into the game -- his third goal in as many games -- and Andrei Zyuzin scored after another man advantage ended for the Flames (3-2-1), who rested top defensemen Robyn Regehr and Dion Phaneuf.
Kiprusoff finished with 36 saves and was at his best against a Canucks power play that failed to capitalize on nine opportunities.
Roberto Luongo gave up two goals on 10 shots through two periods, but stopped all 13 in the third, including Marcus Nilson's breakaway midway through the period.
Calgary center Stephane Yelle left the game midway through the third period and didn't return after taking a low hit along the boards from Canucks defenseman Kevin Bieksa, who was penalized for tripping on the play.