Koivu broke a first-period tie with a power-play goal, and Backstrom made 30 saves, leading Minnesota to a 3-1 victory over Montreal on Thursday night.
Robbie Earl opened the scoring early in the first, and Koivu restored the Wild's one-goal lead later in the period with his 10th goal, tying Andrew Brunette for the team lead. Cal Clutterbuck added his sixth goal in the third.
"Early in the game, you get the lead and you get the team going, and I think it's important on the road," Koivu said. "We did a pretty good job defensively, even if they had a lot of shots. In the third period we tried to keep it tight in the middle, and obviously Backstrom played a great game so that always helps."
Backstrom extended his personal winning streak to four as the Wild won their second in a row. Minnesota is 9-2-1 following a four-game losing streak.
"I think we played a pretty good game," Backstrom said. "The guys on defense did a great job to help me see the puck."
Andrei Kostitsyn scored for Montreal, which has dropped five in a row (0-4-1), including a 2-1 loss at New Jersey one night earlier.
"It's a tough thing we're going through," Canadiens defenseman Hal Gill said. "We've been playing a lot better, we've been in games, we're just coming out on the wrong end of them and we've got to find something to make the difference. We've got to dig a little deeper and get some goals and find a way to capitalize on chances."
Carey Price stopped 18 shots and fell to 2-5-2 in his last nine starts.
The Canadiens held a 31-21 advantage in shots, the first time they have outshot an opponent in 10 games.
"That was our goal, to go and put the puck at the net, and it just didn't go in for us tonight," Gill said.
Montreal's Roman Hamrlik did not play after leaving Wednesday night's game with a knee injury. With Hamrlik out, Montreal's defense was bolstered by the return of Paul Mara, who missed five games because of an upper-body injury.
"We've been hit with the injuries pretty hard," Gill said. "It's tough to get in a rhythm but we've got to find a way to substitute guys in and out and make it as seamless as possible."
Guillaume Latendresse faced the Canadiens for the first time since he was dealt by Montreal to Minnesota on Nov. 24 in return for Benoit Pouliot, who was chosen fourth overall by the Wild in the 2005 draft.
Earl put Minnesota up 1-0 just 2:41 in when he beat Price between the pads with a shot from the right faceoff dot that the Montreal goalie surely wishes he could replay.
The Canadiens responded 45 seconds later to tie it at 1 on Kostitsyn's fifth goal in four games. Scott Gomez began the scoring play when he stripped the puck off Eric Belanger along the boards. Kostitsyn drove the right side and got past Wild defenseman Marek Zidlicky before tucking a backhand past Backstrom for his ninth goal.
Koivu put Minnesota ahead to stay at 14:08 when he redirected Martin Havlat's centering pass in from the goalmouth despite being covered by Canadiens defenseman Josh Gorges.
Clutterbuck gave the Wild a two-goal margin 11:47 into the third when he stuffed a rebound off the end boards inside the right post.
Latendresse failed to record a point after he scored Tuesday night in a 2-1 win in Columbus. It was his first point in seven games after posting two goals and an assist in his first three games with the Wild.
"I was really nervous," Latendresse said. "I think I was more nervous than my first game. It was hard to get over that and get going. I think I was not able to get in my game and it was different than what I'm used to and it's not the kind of game I usually bring in Minnesota."
Pouliot, who was injured with a sprained wrist at the time of the trade, is currently on a conditioning assignment with Hamilton of the AHL and has yet to play with Montreal.
Wild D Clayton Stoner made his NHL debut. Stoner played a total of 22 shifts and saw 14:42 of ice time. ... Latendresse had 48 goals and 85 points in 242 regular-season games with Montreal from 2006-09. ... Canadiens LW Mike Cammalleri played his 400th game. Cammalleri, who has also played with Los Angeles and Calgary, leads Montreal with 18 goals and is second in points with 30. He has 150 goals and 167 assists overall.
Copyright by STATS LLC and The Associated Press
Arena: Bell Centre Location: Montreal, Quebec
Referees: Marc Joannette, Rob Martell Linesmen: Pierre Champoux, Scott Cherrey
Attendance: 21,273 (100.0% full)
Team Stat Comparison
Power Play Goals
Power Play Opportunities
Shots on Goal
Robbie Earl (3)
Assist: Kim Johnsson
Andrei Kostitsyn (9)
Assist: Scott Gomez
Mikko Koivu (10)
(Power Play) Assists: Martin Havlat, Andrew Brunette
No scoring this period
Cal Clutterbuck (6)
Assists: Chuck Kobasew, Nick Schultz