Troy Stecher had a goal and an assist, Backlund and MacKenzie Weegar each had two assists, and Jacob Markstrom made 16 saves for the Flames (35-26-15), who have won three in a row for the first time since Dec. 7 and just the third time all season.
Calgary has won four of its past five games but still trails Winnipeg, which defeated the Detroit Red Wings 6-2 earlier Friday.
"You can look at the standings, where we are and the fight that we're in, so a big two points for us obviously and got to keep this going," Stecher said. "It speaks volumes to the character we have in this room. It seemed anytime we scored we took a step backwards. It's not something you want to do, but at the end of the day we find a way to get two points and stay in the hunt."
Demko made 36 saves for the Canucks (34-34-7), who have at least one point in five straight games (3-0-2) and are 10-2-2 in their past 14. But after tightening up defensively since coach Rick Tocchet took over for Bruce Boudreau on Jan. 22, they have given up 11 goals in their past two games.
"I don't know if it's a structure thing; we've got to win a little more battles," Tocchet said. "Some guys have to get a little more gritty in situations. … We're not there yet and we've got to get to that level. And that's getting stronger, anticipating a little bit, and meeting pressure with pressure. We'll get there but, hey, listen, another point against a desperate team."