Michael Frolik, Mikael Backlund and Sam Bennett each had a goal and an assist, while Sean Monahan also scored for Calgary (23-25-3), which rebounded from a 2-1 home loss to Columbus a night earlier. T.J. Brodie added two assists.
The Flames beat the Canucks in a tight six-game series in the first round of last year’s post-season, but both clubs currently sit outside of the Western Conference playoff picture.
Frolik finished off a nice passing play with Backlund and Brodie on a 3-on-2 rush for his ninth of the season 6:25 into the second period to give the Flames the lead.
Vancouver started to come to life later in the period, with Etem trying Hiller on a wraparound before Henrik Sedin fired just wide from a sharp angle on the power play.
Hamhuis returned to the lineup after missing 21 games with facial fractures. The veteran defenceman, who wore a modified cage against Calgary, took a slapshot to the mouth in a scary incident on Dec. 9 and had his jaw wired shut until early January.
After the Flames had a goal waved off because of a hand pass eight minutes into the third, Monahan put the game to bed with his 16th of the season at 15:07 on a one-timer from the slot that beat Miller over the blocker.
The Canucks, who lost 2-1 to Columbus in a shootout on Thursday, pulled Miller for an extra attacker, but Backlund scored his sixth into an empty net with 2:15 left.
Etem, with his first of the season, got a consolation goal at 18:26, but Vancouver fell to 1-3-2 over its last six.
Bennett scored another empty-net goal, his 14th, with 35.9 seconds left.
The shots were just 7-5 in favour of the Flames after a scoreless and sleepy first. Calgary's best chance came about five minutes in when Miller stopped Matt Stajan's backhand effort on a breakaway, while Alexandre Burrows came closest for Vancouver when his shot hit the post and stayed out near the midway mark of the period.
Notes: The Canucks have just one regulation victory in their last 11 games. ... Vancouver defenceman Yannick Weber cleared waivers and was assigned to the AHL's Utica Comets earlier Saturday. Weber joins wingers Chris Higgins and Brandon Prust as veterans the Canucks have demoted to the minors in recent weeks in favour of younger players. ... Vancouver visits Colorado on Tuesday, while Calgary hosts Toronto.