The Canucks came in having lost four straight by identical 5-2 scores, a first for an NHL team, and were 0-5-1 over their last six at Rogers Arena.
Playing their second game in as many nights after Saturday's 3-2 victory in Edmonton, the Avalanche trailed 3-0 after two periods, but could have easily been ahead if not for Miller's stellar play.
Colorado, which occupies the first wild-card spot in the Western Conference, had a couple of good early chances before the Canucks grabbed the lead at 8:31 of the opening period. Cracknell, who went 28 games without a goal prior to scoring in Friday's loss in Calgary, stopped Emerson Etem's shot in front of Varlamov and shovelled home his fifth of the season and first on home ice.
Vrbata rang a shot off the post behind Varlamov that stayed out before Miller stoned Carl Soderberg with a pad stop for his biggest save of the period after some great work from Nathan MacKinnon.
Hansen then made it 2-0 with 1:14 left in the first when he buried a Daniel Sedin pass from behind the net for his 18th for Vancouver, which sits seven points back of Nashville for the West's second wild-card spot.
Miller was strong again in the second, stopping Soderberg on a short-handed breakaway and snagging a Jarome Iginla one-timer on the power play.
The Vancouver goalie was fortunate when Francois Beauchemin's shot hit the crossbar and stayed out midway through the second.
Cracknell appeared to score his second of the night at 12:17, but it was ruled after video review that he directed the puck in with his glove.
Miller stoned Erik Johnson with a brilliant toe save on a 3-on-2 to keep his team up by two and set the stage for Vrbata's power-play goal with 4.4 seconds left in the second. The veteran forward had not scored in 14 games and had just one over his previous 24, but poked a rebound past Varlamov for his 12th.
Colorado's Blake Comeau hit the post early in the third period, but Hansen scored his second of the night and 19th of the season at 9:09 when he redirected Daniel Sedin's pass on a 2-on-1.
Avalanche head coach Patrick Roy pulled Varlamov for an extra attacker with more than 10 minutes left in regulation, but Tanev scored his fourth into the empty net at 11:37 to seal it.
Duchene broke Miller's shut-out bid with 41.8 seconds left to round out the scoring with his 26th.
Notes: Vrbata and Derek Dorsett left in the third period for Vancouver and did not return. ... The Avalanche acquired former Canucks forward Shawn Matthias from Toronto in a trade Sunday for a 2016 fourth-round pick and prospect Colin Smith. Matthias is expected to join the team later this week.