Blake Comeau, Mark Letestu and R.J. Umberger also added goals to help the Blue Jackets remain in the thick of a tightly packed playoff chase. They pulled even in points (47) with Detroit for the final playoff spot.
Cody McLeod scored twice and Jamie McGinn added another for the Avalanche, who are last in the Western Conference.
Foligno skated in on the right side of Jean-Sebastien Giguere and sent a wrist shot by the veteran goaltender.
Moments before, Bobrovsky came up big when he turned aside a shot by Gabriel Landeskog, who broke free with the Avalanche short-handed.
McGinn gave the Avs a lead with just over two minutes remaining in regulation on a power play, but it didn't hold as Umberger answered just 35 seconds later.
Columbus was cruising along after Comeau's goal early in the third period gave the team a 2-1 lead, before Bobrovsky was bumped to the ice by McLeod.
Tyson Barrie quickly gobbled up the puck in the corner and sent a shot toward the net. McLeod redirected the puck past a sprawled-out Bobrovsky, who quickly looked toward the referee for an interference call.
This was McLeod's first two-goal game since Oct. 17, 2009, at Detroit. The small number of fans who braved a spring snow storm roaring through the Mile High City let out a thunderous cheer.
Lately, Colorado hasn't been playing as if it's a last-place team. Giguere woke his teammates out of their funk when he criticized them for being more concerned about postseason plans in Las Vegas than their play on the ice.
That seemed to do the trick. Colorado is 2-0-2 following Giguere's outburst.
There also was a dose of motivation for the Avs, too. The Blue Jackets beat Colorado twice down the stretch last season, all but ending the team's late playoff bid.
This time, the Avs were trying to step into the role of spoilers.
After a rather uneventful opening 20 minutes, the action picked up in the second, featuring plenty of scoring chances and a few punches.
McLeod gave the Avalanche a 1-0 lead when he knocked in a loose puck after Bobrovsky stopped a Landeskog liner.
The lead didn't last as the Blue Jackets took advantage of a fortuitous bounce when Vinny Prospal tried to clear the puck around the boards, only to have it wind up right back on his stick off a bizarre carom. He quickly found an open Letestu, who beat a stunned Giguere.
Soon after, Brad Malone and James Wisniewski dropped the gloves and squared off at center ice. The brawl didn't last long and both were escorted into the penalty box.
Columbus came up big late in the period, withstanding 4 minutes of penalty time on Marian Gaborik for a high stick that drew blood on defenseman Matt Hunwick.
Gaborik nearly scored midway through the first period, but his shot from the side of the net hit Giguere in the chest.
NOTES: Colorado coach Joe Sacco will lead the U.S. squad at the International Ice Hockey Federation World Championship in May. The tournament will be held in Helsinki, Finland, and Stockholm, Sweden. ... Colorado reassigned G Sami Aittokallio to Lake Erie of the American Hockey League before the game. ... Avs prospect Gus Young helped Yale to a win over Quinnipiac on Saturday in the NCAA championship game. Young, a seventh-round pick in 2009, is a defenseman and was on the ice for all four goals. ... Blue Jackets F Artem Anisimov was scratched with an upper body injury. He was hurt Saturday in Minnesota on a hit. ...A moment of silence was held before the national anthem for the victims of the bombings at the Boston Marathon earlier Monday.