The Wild had not won in Columbus -- going 0-6-3 -- since their only other win on the Blue Jackets home ice, way back on Jan. 18, 2002.
"It's been a long time. We don't win here too often," Wild coach Jacques Lemaire said. "They have a team pretty much like us. They play hard and every game is a close game."
Rolston snapped a 1-1 tie with a hard slap shot from the top of the left circle that slipped inside the near post and past goaltender Pascal Leclaire at the 2:22 mark of the third period.
"I just wanted to get it on the net," Rolston said. "I think it might have hit off of one of their defensemen in front. It was just good luck, basically."
Backstrom did the rest, handling a flurry of shots in the final minutes while the Blue Jackets desperately looked for the tying goal.
"We started the game real slow," Columbus forward Jason Chimera said. "We got our legs in the third period. We came out and got lots of chances. Unfortunately, we ran out of time. We got it going too late."
Aaron Voros also scored for the Wild, who had been shut out 5-0 by Detroit's Dominik Hasek on Friday night and had mustered just three goals in their last three games.
"We just came out flat and didn't show any signs of life last night," said captain Mark Parrish, who had a second-period goal waved off Saturday night by a quick whistle. "Obviously, we talked about it in here and wanted to come out to prove that we are willing to work hard."
Nikolai Zherdev scored for Columbus, giving him four games in a row with a goal. It was his 11th goal in his 29 games this season; he had 10 in 71 games a year ago.
The game pitted the NHL's two newest franchises, admitted to the league for the 2000-2001 season.
Minnesota went up 1-0 at the 13:51 mark when Marian Gaborik controlled the puck off the wall near center ice and passed to Pavol Demitra, who skated in unimpeded from the right wing. Leclaire committed to Demitra, who slipped a quick pass through the crease to Voros at the other side of the net, who jammed it in for his fifth goal.
For years Rolston and Demitra have been thorns in the Blue Jackets' side. Rolston has seven goals and 11 assists in 16 games against Columbus, while Demitra has 32 points in 28 meetings with the Blue Jackets.
The Blue Jackets evened it a minute into the second period off Chimera's backhanded setup pass to Zherdev at the right circle, where he blistered a one-timer past Backstrom.
In the waning moments, Backstrom turned away several prime Columbus scoring attempts.
"Tonight we played about 12 minutes of the way we have to play -- that's what happens when you put skill ahead of work," said Blue Jackets coach Ken Hitchcock, prevented from winning his 450th career game in the NHL. "We've been guilty of that for a couple of nights now and tonight it caught us."
Injured Columbus RW David Vyborny (hip) was honored before the game for playing in his 500th NHL game earlier this season and also for passing 300 career points, all with Columbus. ... Gaborik has points in six of his last seven games, with three goals and three assists over that span. ... The Wild was 0-for-4 on the power play and is now 1-for-24 over the last six games.
Copyright by STATS LLC and The Associated Press
Arena: Nationwide Arena Location: Columbus, Ohio
Referees: Stephane Auger, Kevin Pollock Linesmen: Lonnie Cameron, Steve Miller
Attendance: 15,666 (86.4% full)
Team Stat Comparison
Power Play Goals
Power Play Opportunities
Shots on Goal
Aaron Voros (5)
Assists: Pavol Demitra, Marian Gaborik
Nikolay Zherdev (11)
Assists: Jason Chimera, Michael Peca
Brian Rolston (9)
Assists: Kim Johnsson, Pierre-Marc Bouchard