From the opening face off of the middle period, Gaborik broke down the right side, took a pass from Pavel Demitra and sent a wrist shot from 15 feet that went between Curtis Joseph's pads and into the net 12 seconds into the period. It was Gaborik's 14th goal of the season and third in his last two games.
"We had good fortune with our line," Gaborik said. "Pavel gave me a great pass and I was able to flip it in."
Gaborik's goal set a franchise record for the fastest tally at the start of a period. Wes Walz set the previous mark, 20 seconds into a period, on Dec. 8, 2001, at Philadelphia.
With an airtight defense and Backstrom's stellar goal keeping, Gaborik's score was all Minnesota needed. Backstrom was filling in for the injured Manny Fernandez, who is expected to be out two to three weeks with a sprained knee.
"The guys played a terrific game in front of me," Backstrom said, who recorded his other shutout this season against Phoenix. "The forwards were backchecking, and the defense cleared the slot in front of me. Everyone was working together and that was a big part of the win."
The Coyotes had a goal disallowed at 15:36 of the first period. During a goal-mouth scramble, Oleg Saprykin redirected the puck behind Backstrom with his right skate. After a video review, referee Dan O'Halloran waved off the goal.
Despite a strong effort, the Coyotes were shut out for the seventh time this season. Still, their energy and discipline received praise.
"What happened was not from a lack of effort," Joseph said. "We crashed the net pretty hard and that is what you have to do to score. We just didn't get a break."
The Coyotes came close to tying the game twice in the second period.
Yanic Perreault broke in alone behind the defense in front of Backstrom, but only managed a weak shot with under 7 minutes remaining. Then Patrick Fischer took a feed from Perreault, but was denied by Backstrom with 4 minutes left.
Phoenix couldn't capitalize on a power play late in the game. With the Keith Carney off for interference at 15:57 of the final period, Backstrom stopped Steven Reinprecht in the Coyotes' only good shot.
"This was a real tough loss," Phoenix coach Wayne Gretzky said. "We did many good things, and played against a very good hockey team. This was disappointing because the work ethic from our guys was really strong."
Backstrom preserved the shutout in the final seconds when he deflected Phoenix defenseman Zbynek Michalek's blast from the right side.
Phoenix is 12 points behind Minnesota for the final playoff spot in the Western Conference. ... Prior to the game, Minnesota recalled defenseman Shawn Belle from Houston of the AHL. In eight games earlier this season with the Wild, Belle picked up one assist and no penalty minutes.