The Blue Jackets, 24th in the NHL on the power play, scored twice in eight man-advantage chances while the Red Wings were 0-for-6. Norrena had a big night in goal, a day after Columbus tied a franchise record by being shut out for the 11th time this season.
With the Red Wings trailing 2-1 and buzzing the net late in the game, Foote provided the insurance goal when his blast from the point hit off Detroit defenceman Chris Chelios' leg and slipped past a surprised Dominik Hasek.
Johan Franzen scored at the 4:53 mark of the third to end Norrena's shutout. The Red Wings, down 2-0 at the time, own the longest streak of consecutive games without a shutout in the NHL at 169 games. They have not been shut out in more than three years.
Columbus took a 1-0 lead at 16:40 of the first when Hasek stopped Manny Malhotra's hard shot, only to have Fritsche pounce on the rebound and jam it in for his ninth of the season.
Each team failed to score on prime chances in the opening period. Kris Draper's blast from the top of the left faceoff circle hit the far post and almost crossed the goal-line before Norrena fell backwards on top the puck.
That was waved off after a video review, just as an earlier Fritsche attempt was ruled no goal under almost identical circumstances. Hasek ended up laying on his back in the paint as if he were creating snow angels while Fritsche dug at the puck underneath the small of the goalie's back.
Midway through the second period, Detroit defenceman Nicklas Lidstrom picked up a four-minute double-minor for high sticking his former teammate, Sergei Fedorov, who cupped a hand over his bleeding left ear as he went to the penalty box.
Soon after, Foote's slapshot was redirected by Svitov for his fifth of the year.
The Blue Jackets were on their third consecutive power play later in the period when Chelios inexplicably slid a pass in front of his own net where a stunned Svitov fanned on the shot.
The Red Wings cut the lead while each team was a man down. Lidstrom was on the short boards and passed to Niklas Kronwall for a hard shot from the point. Norrena blocked the shot, but Franzen was there to clean up for his fifth.
Notes: Columbus RW Nikolai Zherdev, slumping with only one goal in his last 21 games, was a healthy scratch . . . Detroit D Mathieu Schneider missed his sixth consecutive game with a knee injury . . . The Blue Jackets are 7-20-7 all-time against the Red Wings . . . Detroit's Henrik Zetterberg and Tomas Holmstrom each have six-game points streaks come to an end.