Chris Higgins, Alexandre Burrows, Daniel Sedin and Cody Hodgson also scored for Vancouver (6-5-1), which kicked off a six-game road trip.
Alex Tanguay scored the lone goal for Calgary (4-5-1), ruining Luongo's shutout bid with 32 seconds left in the game.
Luongo was coming off a miserable October in which he went 3-3-1 with a 3.54 goals-against average and a meager .869 save percentage.
Edler's assists came in the first period as the visitors silenced the Saddledome crowd by scoring a pair of power-play goals in the final 7 minutes to open up a 3-0 lead.
Vancouver opened the scoring 7:57 into the first period when Higgins took a breakaway pass from Jannik Hansen and cleanly beat Miikka Kiprusoff with a backhand under the crossbar. It was Higgins' team-leading sixth of the year.
The Canucks made it 2-0 at 13:42 on the power play when Burrows swiped the puck in while sitting near the crease. The goal came at the end of a power play after Calgary successfully killed off a 1:36 two-man advantage in which Burrows put a shot off the goal post.
Vancouver got another power play in the final minute of the period and needed just 14 seconds to convert, as Daniel Sedin scored at 19:41 after being set up by brother Henrik.
Despite getting outshot 12-4 in the second period, Vancouver scored the only two goals to blow open the game.
The Canucks made it 4-0 at 3:47 when Flames defenseman Mark Giordano left Hodgson uncovered for an easy goal into an empty net after a nice feed from Maxim Lapierre.
Edler scored Vancouver's fifth goal at 11:27 with a slapshot from the blue-line with Hodgson screening Kiprusoff.
Edler has 12 points on the season, which ranks him third amongst NHL defensemen behind co-leaders Erik Karlsson from Ottawa and Tampa Bay's Marc-Andre Bergeron.
Vancouver improved to 10-0-2 against the Flames since last losing in regulation to Calgary on Oct. 16, 2009. That includes five straight victories in Calgary by a combined score of 24-8.
Luongo improves his career mark against Calgary to 21-10-3.
Calgary was 0-for-5 on the power play to fall to 2-for-27 in its last seven games. The Canucks were 2-for-6.
It was the finale of a season-long six-game homestand for Calgary. The Flames finished 3-2-1 and now head out on a three-game road trip that begins Thursday night in Detroit.
It was Sedin's 254th career goal, tying him with Pavel Bure for fourth on the Canucks all-time list. ... Calgary C Matt Stajan was back in the lineup after being a healthy scratch the previous two games. ... Calgary LW Curtis Glencross played in career game No. 300. ... The Flames began a stretch of seven games in 12 nights.