Columbus seemed on its way to a crucial loss in its push for a Western Conference playoff spot, trailing 3-2 with 1:27 remaining in regulation.
But R.J. Umberger forced overtime with a tally and Foligno later completed the comeback as the Blue Jackets pulled even with eighth-seeded Detroit at 47 points with their fourth straight win.
The Red Wings own the tiebreaker between the clubs.
Cody McLeod netted two goals and Stefan Elliott also scored for the Avalanche.
Jean-Sebastien Giguere made 26 saves for Colorado.
Celebrity Families of 2014 [PHOTOS]