Gabriel Landeskog and Steve Downie each had a goal and an assist and Matt Hunwick also scored for the Avalanche, who were up to their usual tricks against the Blue Jackets. They are 32-8-1-1 against Columbus, including 15-5-1-1 on the Blue Jackets' home ice.
The Avalanche won a second game in a row for the first time since Dec. 31. They started the night two points out of the eighth playoff spot in the West.
Varlamov made several sterling stops to keep Colorado in command until they closed it out with two third period goals.
The game was the first for the Blue Jackets since they made two major trades this week.
It was Varlamov's third shutout of the season and ninth of his career. He added to his career high with his 17th win of the season.
On Wednesday the Blue Jackets traded center Antoine Vermette to Phoenix for a 2012 second-round pick, a conditional fifth-rounder in 2013 and injured goalie Curtis McElhinney. Then on Thursday night they sent second-leading goal scorer Jeff Carter to Los Angeles for defenseman Jack Johnson and a conditional first-round pick.
Johnson arrived at Nationwide Arena during the second period for his physical and received a loud ovation when he was introduced to the crowd in the third period.
It was one of the few times Columbus fans had anything to cheer.
In the final minute of the opening period, the Blue Jackets' Colton Gillies took a centering pass from Ryan Johansen and his shot clanged off the crossbar. It bounded all the way to the point where it was collected by Jones to begin a 2-on-1. He then converted with a low wrister from the right dot that beat goalie Steve Mason on the stick side for his 13th of the season, unassisted.
Landeskog notched his 16th of his brilliant rookie season midway through the second period. He took a cross-ice pass from Downie and set himself for a wrister from the right dot that beat Mason high on the glove side just inside the far post.
Varlamov then prevented the Blue Jackets from drawing closer.
First, he stymied Rick Nash — the subject of numerous trade rumors which have him offered to almost every team in the league — on a 2-on-1 rush pass from Ryan Johansen from point-blank range.
Then Nash took a stretch pass and roared in on the net by himself. Nash faked the forehand and tried to slip a backhand around Varlamov, but his left toe save kept the Blue Jackets off the board.
The Avalanche pushed the lead to 3-0 on Jones' second of the night early in the third period. Mark Olver sent a pass to him from the back boards and Jones whiffed on his first attempt as defenseman Fedor Tyutin attempted to block the shot, but he reset and scored on his second try.
Downie pounced on a rebound and Hunwick turned a turnover into an end-to-end sprint for third period goals to add to the lopsided margin in the third period.
Mason — and his teammates — were loudly booed after each of those goals.
Notes: The Blue Jackets called up RW Cam Atkinson earlier in the day, and he made his first appearance with the team since Nov. 5. ... Scouts representing Boston, Philadelphia, New Jersey, the New York Rangers, San Jose, Pittsburgh and Tampa Bay took in the game less than 72 hours before the trade deadline. ... Colorado came in with the NHL's best road power play but was scoreless in its only chance with a man advantage.