Horvat scored 4:12 into the third on a power play when he swatted in a centering pass from Ben Hutton. Shortly after, former Canucks defenseman Matt Bartkowski got caught flat-footed in the neutral zone, enabling Henrik and Daniel Sedin to break in dangerously, with Daniel setting up Henrik.
''I feel better than the last couple years,'' said Henrik Sedin, 37, who last scored on March 23, 2017. ''We've created enough chances for me to put the puck in the net. Early in the season you need bounces to get goals early and I haven't gotten that.''
''It definitely wasn't our best game. It wasn't like we dominated 60 minutes,'' Horvat said. ''But we scored at the right time and made big plays at the right time.''
Dougie Hamilton, Johnny Gaudreau and Micheal Ferland scored for Calgary, which ended a three-game winning streak. The Flames are 3-2-0 with two games left on a season-long seven-game homestand. Detroit visits Thursday.
Tied 1-1 after the first period, Calgary took the lead twice in the second but was unable to hold it each time.
Gaudreau's power-play goal at 11:51 made it 2-1. The Canucks answered at 15:09 when Vanek ripped a 35-foot slap shot into the top corner.
The Canucks scored a short-handed goal tie it 3-3 when Sutter had his centering pass bounce into the open net off Dorsett's leg.
With backup goalie Anders Nilsson away from the team and with his wife, who is about to give birth, Markstrom got the start once again after losing 3-2 to Detroit on Monday night.
The tall Swede was solid, finishing with 29 saves.
Calgary's Mike Smith was beaten five times on 21 shots.
NOTES: Flames RW Jaromir Jagr (groin) returned after missing six games. To make room, Matt Stajan was a healthy scratch. ... Vancouver C Brendan Gaunce (shoulder) was activated off injured reserve and made his season debut. He took the spot of C Markus Granlund (upper body), who was hurt in Monday's loss to Detroit. ... Vanek played in his 900th game.
Canucks: Play at Anaheim on Thursday night.
Flames: Host Detroit on Thursday night.
More AP hockey: https://apnews.com/tag/NHLhockey
Copyright 2017 by STATS. Any commercial use or distribution without the express written consent of STATS is strictly prohibited.