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DETROIT, MI -- Mikael Backlund scored the game-winning goal and Chad Johnson made 20 saves to help the Calgary Flames to a 3-2 win against the Detroit Red Wings at Joe Louis Arena on Sunday.

Garnet Hathaway and Matt Stajan also scored, and Dougie Hamilton had three assists for the Flames, who have won three of their past four games and two of three without injured forward Johnny Gaudreau (finger).

"Our third and four lines chipped in with goals," Stajan said. "If you can get goals from throughout you're going to have some success.

"They're a patient team. They're fast. They're great off the rush. There are some things we want to clean up for sure but [Johnson] made some big saves for us and our penalty kill was good and we found a way on the road.

"Sometimes you just have to find a way."

Gaudreau, who led the Flames in scoring at the time of the injury, sustained a fractured finger against the Minnesota Wild on Tuesday.

"We've already addressed that in our room, that we need to score by committee," Calgary coach Glen Gulutzan said. "We need to play in 3-2, 2-1 games. We talked about it. It's going to help us evolve as a young group to learn what it takes on a nightly basis to consistently win in this league, and this injury to Johnny, we're trying to spin as a chance to grow in other departments.

"That's what these tight games do for you."

Tomas Tatar and Anthony Mantha scored, and Jimmy Howard made 23 saves for the Red Wings.

Backlund put the Flames ahead 3-2 after swatting a return pass backdoor from Michael Frolik by Howard at 12:14 of the third period.

"We need to chip away," Gulutzan said. "I've really liked our game's come even though the wins are lagging. We're looking at these little segments and trying to put together a run."

Tatar gave the Red Wings a 1-0 lead at 8:06 of the first period. Justin Abdelkader's shot was blocked by TJ Brodie, but Tatar shot the rebound through a screen and between Johnson's pads.

Hathaway scored his first NHL goal 3:40 into the second period to tie the game 1-1. Hamilton one-timed a pass from Micheal Ferland that deflected off of Hathaway in the crease and behind Howard.

"We're all working down there and [Ferland] gets it out, pulls it up to Dougie," Hathaway said. "I'm just going as hard as I can there. Howard was flopping around, so I thought maybe it happened. I knew it went that way but I didn't know it went in.

"Not how you draw it up.

"I'll probably say I sniped it.

"It feels amazing. Something I've dreamed off for a long time. I'm happy to help the team win, too."

Johnson stopped a shot from Danny Dekeyser that was redirected in the slot at 15:11, and slid across to stop Henrik Zetterberg's change with three minutes remaining in the second period to keep the Flames tied.

"Every night he's making the saves we needed him to make," Gulutzan said. "Couple big ones at the right times. That helps."

Stajan scored his first of the year to put Calgary up 2-1.Hunter Shinkaruk retrieved a dump-in, and Stajan deflected Hamilton's shot by Howard 2:31 into the third.

"It's nice definitely to chip in," Stajan said. "I've felt good all year. I felt our line has been pretty good all year, whoever we've been playing with, so to get rewarded tonight … it's a big win. We've got to keep pushing. It's a good bounce-back win."

Mantha tied the game just over four minutes later. After fanning on a cross-ice pass on an odd-man rush, he pulled the puck off the boards and circled out from behind the net before lifting a shot short-side over Johnson's shoulder to even the score 2-2 at 7:59.

NOTES: Johnson made his fourth consecutive start. Troy Brouwer led the Flames with four hits. Dennis Wideman was second with three. Wideman also led the Flames in ice time at 25:12. Defenseman Jyrki Jokipakka and forward Linden Vey were scratched for the Flames.

UP NEXT: The Flames visit the Buffalo Sabres at KeyBank Center on Monday (5 p.m. MT; SNW, SNW, SN960).