DETROIT -- It was the kind of game only a hockey fan could appreciate, as far as Detroit Red Wings coach Mike Babcock was concerned.

But, considering the way injuries are mounting and the amount of travel his team has done lately, Babcock couldn’t complain too much about his team’s 6-5 overtime victory Saturday night over the Columbus Blue Jackets at Joe Louis Arena.

Johan Franzen sent fans home happy by taking a pass from Henrik Zetterberg and whipping in a wrist shot from the slot 45 seconds into overtime.

“I’m pleased to get points,’’ Babcock said. “I thought our guys hung in there. If you’re a fan, it’s an exciting game. If you’re a coach or a player, a ton of mistakes both ways.

“It was ugly around both teams’ nets and yet you got to give (Zetterberg) and Mule (Franzen) credit. They had just been out for the tying goal and then went out and got the win.’’

The Red Wings responded after Rick Nash tied it with 1:04 to play in regulation. It was Franzen’s 19th goal.

“Hank had the puck in the corner and I was taking a little curl up the blue line to shake the (defenseman) off,’’ Franzen said. “They kind of lost me. I skated down the middle and no one seemed to find me, except for Hank, of course.’’

Joey MacDonald, subbing for injured goalie Jimmy Howard, won his first NHL game in more than a year.

Detroit’s grinders stepped up big, as Drew Miller had a goal and two assists, his first career three-point game, and posted a plus-4 rating. His linemates were good, too, as Kris Draper scored a goal and recorded his 200th assist and Darren Helm continued his strong play with a pair of assists. Jonathan Ericsson had a goal and an assist. Valtteri Filppula and Brian Rafalski also scored goals for the Red Wings.

After playing well the last two games in relief of Howard and having nothing to show for it, MacDonald will take a win any way he can get it. His last NHL victory also came against Columbus, on Dec. 3, 2009, when he played for Toronto (6-3). His only other win with the Red Wings came on Feb. 11, 2007 (7-4 vs. Calgary).

“As a goalie, you don’t want to give up five goals, but it was one of those games,’’ MacDonald said. “I look at the other end, the same thing happened to (Steve) Mason. Pucks were bouncing off things and going in off shin pads. It was just one of those nights you throw pucks at the net and you don’t know what’s going to happen.

“There’s a couple of goals I’d like to have back. I think I was down a little bit on a couple of them. But you know what, (playing) back-to-back nights, everybody’s kind of tired. We get the win, that’s the main thing.’’

The Red Wings were fortunate to once again have the firepower to come back, despite missing a large chunk of their offense (Pavel Datsyuk, Danny Cleary, Tomas Holmstrom) to injuries.

“We don’t have Datsyuk out there dangling around or Tommy tipping pucks, so we got to get them in there somehow,’’ Miller said. “We were shooting them from everywhere, more pucks from the sides below the goal line. They create rebounds and we can get the buzz going around in their zone.’’

Ericsson tied the game at 3:57 of the second period, banking in a shot off Mason from behind the goal line. Rafalski snapped a 3-3 tie at 8:02 of the second period. Draper snapped a 4-4 tie at 3:32 of the third period by knocking in a rebound with one hand.

“I thought Helm’s line was fantastic,’’ Babcock said. “We got a great game out of Miller, Helm and Draper and I thought Abby’s line (Justin Abdelkader with Jan Mursak and Tomas Tatar) was good as well. So we’ve been getting great support from those guys.’’

Said Helm: “We’re just doing a good job turning pucks over, using our speed and getting pucks to the net. Millsie had a great game, he’s doing a lot of good things. Drapes had a nice goal. We just played well together as a line.’’

The Red Wings rallied after a slow start, getting goals from Filppula and Miller 1:46 apart late in the first period to tie it 2-2.

The Blue Jackets jumped out to a 2-0 lead less than five minutes into the game on goals by Derick Brassard and Grant Clitsome. They took a 3-2 lead at 2:57 of the second period on a breakaway by Matt Calvert.

It was the third game in a row and the fourth time in the last five games the Red Wings have trailed by two goals. But they battled back once again.

“We kind of wanted to win (Friday), but we didn’t get it (3-2 shootout loss in Columbus),’’ Franzen said. “We got one tonight. Three points in two days was kind of fair.’’