The very good Red Wings were on display for 60 minutes in Nationwide Arena, and behind 28 saves from Jimmy Howard defeated the Blue Jackets 5-0.
"Two of the last three games have been good," Babcock said. "It's the consistency that you're looking for."
Howard stopped 20 shots through two periods and the Red Wings built on goals by Tomas Tatar and Gustav Nyquist with goals 72 seconds apart in the third by Tomas Jurco, on the power play, and Riley Sheahan. Darren Helm scored his second of the season with 61 seconds left.
Detroit (9-4-5) won for the first time in its past four road games. Columbus (6-11-1) had won two in a row following a nine-game losing streak.
Howard got his 19th career shutout in his 300th NHL game, all with the Red Wings; he is 160-89-41.
"When you look at the score afterward you see 5-0 and say that's no contest," Babcock said. "That's not the case at all. Jimmy was real good for us. He gave us a chance."
Howard preferred talking about the way Detroit responded to the Montreal defeat rather than his personal achievements.
"We all knew we didn't play very good, but over the course of season those things are going to happen," the 30-year-old said. "I thought we did a great job of bouncing back tonight."
The Blue Jackets might dispute that Howard had a shutout at all. After Tatar gave Detroit a 1-0 lead, Columbus used the first power play of the game to temporarily get even with 1:42 remaining in the first period.
Boone Jenner skated out of the left corner and powered his way toward the crease. Draped by Detroit defenseman Niklas Kronwall, Jenner was falling to the ice but stuck his leg out and knocked the puck past Howard with his skate.
"On the original play, I thought it was a goal just because there was a little bit of a pileup and I didn't see where the puck went after he jammed it off me," Howard said. "I was trying to find the puck, and the next thing you know I hear the cannon going off.
"When they showed it on the screen you could tell it was a pretty distinct kicking motion."
The original call of a good goal was overturned after video review.
"That was a really tough call to make when his leg motion was going to the net," Columbus center Ryan Johansen said. "There's nothing you can do about it."
Blue Jackets defenseman Jack Johnson said there was little frustration about not tying the score.
"We were hoping to turn it around and score immediately," he said. "We still had a lot of time on the power play; 'Let's get another one.' It was still the first period. We never thought in a million years we would get shut out tonight."
The Red Wings made it 2-0 on Nyquist's power-play goal 1:44 into the second period. His ninth goal came off a lengthy rebound that Columbus goalie Sergei Bobrovsky stopped with his left pad but was unable to corral.
"We came out in the second and were flat," Jenner said. "We weren't sharp, as intense. They were better than us. In the third we need to make a better push than that."
Detroit put the game away when Johansen was goaded into a roughing penalty on Kyle Quincy and Jurco scored eight seconds later off a Detroit faceoff win at 4:49 of the third period.
"It was a bad penalty on my part. I can't take that," Johansen said.
Jurco used a wrist shot from the left circle to score for the first time in 15 games this season.
"It was an amazing feeling," he said. "It's been so long since I've scored I couldn't believe it at first."
Howard could sense the pressure had been lifted from Jurco.
"You could see the relief on his face on the big screen," Howard said.