The Blue Jackets won their third straight and pulled even with Detroit and Dallas for the eighth and final playoff spot in the Western Conference with 45 points.
The Wild dropped their third straight and were left clinging to a two-point lead over the Red Wings, Stars and Blue Jackets with 47 points.
"You aren't going to complain about a win or anything like that, but we've got to be a lot better," Richards said after watching his Blue Jackets spend most of the night in their own zone while Minnesota dictated the pace.
But the Wild couldn't solve Bobrovsky, and the Columbus offense needed only a six-minute stretch in the second period to take the lead.
Still, Yeo tried to keep an upbeat tone, lauding his team's resolve.
"The bottom line is that's a big point for us," Yeo said. "When you're down and their goalie is playing like that, to tie it up late, that's a big point."
Pominville's third-period goal made it 2-all after the Wild offense had controlled most of the game. It was a far cry for Columbus from the previous night, when the Blue Jackets snapped St. Louis' six-game winning streak.
"I think they definitely had a little bit more jump than we did tonight," Blue Jackets defenseman Jack Johnson said. "I think we played better last night than we did tonight. Sometimes you got to win games that you shouldn't."
The Wild broke a 137-minute scoring drought late in the first period when Bouchard tipped the puck after Brett Clark sent it toward the net from the left circle.
The puck went off Johnson's skate past Bobrovsky, and Bouchard was credited with his fifth goal of the season to put Minnesota up 1-0 at 15:59.
Prospal tied it nearly four minutes into the second off a pretty backhand pass from Brandon Dubinsky from behind the net.
Two minutes later, Tyutin put Columbus up 2-1 with a slap shot from the left circle at 6:18.
Things got heated in the opening seconds when Brandon Dubinsky went at Wild C Charlie Coyle for leveling Artem Anisimov with his shoulder. Coyle was assessed a match penalty and ejected, and Dubinsky was given a 10-minute major for instigating. Afterward, Yeo said he thought the hit was clean, and that the Wild should've had a power play due to Dubinsky's instigating. The fight was the first of Coyle's NHL career. ... Anisimov did not return to the game. ... Tyutin played in his 600th game of his career. ... Wild C Matt Cullen (lower body), F Dany Heatley (shoulder) and C Zenon Konopka all sat out injured. Earlier in the day, Cullen practiced for the first time since getting hurt April 1. Yeo said Cullen would accompany the team on the upcoming three-game road trip. ... Columbus F and former Wild star Marian Gaborik was booed in pregame introductions and nearly every time he touched the puck.
Copyright by STATS LLC and The Associated Press
ST. PAUL, MN - APRIL 13: Jason Pominville #29 of the Minnesota Wild warms up prior to the game against the...