Detroit (12-20-4) also defeated Columbus 3-1 here Saturday after being outscored 12-1 in its previous three games.
"I thought this was a great performance," Red Wings coach Jeff Blashill said. "These guys looked in the mirror after the game on Thursday (7-1 loss to the Nashville Predators) and they showed up ready to practice their tails off on Friday. Then they worked this hard for back-to-back games. That's four days without a break.
"This group really wants to be a better team."
Calvin Pickard made 16 saves in his second consecutive start.
"I think [Pickard] has been the X-factor for us this weekend," Red Wings captain Dylan Larkin said. "Every time they got a chance, he swallowed it up. He was rock-solid and he didn't give up any rebounds."
Jack Roslovic scored, and Elvis Merzlikins made 25 saves for Columbus (13-15-8), which is 0-3-1 in its past four games.
"We played awful," Blue Jackets coach John Tortorella said. "A ton went wrong. I think we played harder (than Saturday), but we couldn't make a play."
Evgeny Svechnikov gave the Red Wings a 1-0 lead at 10:40 of the first period, beating Merzlikins blocker side from the high slot.