Todd White also scored for the Wild, who set the team record for victories in a season with 43 and pulled within one point of Vancouver in the Northwest Division race.
The Coyotes made things interesting when Brendan Bell and Bill Thomas scored power-play goals in the first 10 minutes of the third period to cut Minnesota's lead to 3-2, but they never threatened again and lost their fourth straight.
Curtis Joseph had a rough night in net for Phoenix, which lost its fourth in a row and showed its youth by allowing all three goals in the final minute of action in the first two periods.
Phoenix was competitive with the surging Wild for the first 19 minutes of the first and second periods, but lost focus in the waning seconds of each to let the game slip away.
A forgettable first period ended with a flourish when Gaborik grabbed a loose puck near the Minnesota blue-line with under 20 seconds to play.
One of the fastest skaters in the NHL, Gaborik rushed up ice and put a double deke on defenceman Derek Morris before ripping a wrist shot off Joseph's left leg. Demitra grabbed the big rebound and put the Wild on the board with 6.7 seconds to go.
It was still 1-0 for the first 19:17 of the second before Pierre-Marc Bouchard found White in the slot. His shot squirted through traffic in front of Joseph and into the net, prompting the 39-year-old netminder to fall on his back and stare at the overhead goal cam in disbelief.
Twenty seconds later, Demitra slipped a pass across the crease to Gaborik, who fanned on the one-time attempt. But the puck glanced off his skate and trickled slowly in between CuJo's left skate and the post for a 3-0 lead.
It's been that kind of season for coach Wayne Gretzky and the Coyotes, who entered the season with high hopes after acquiring veterans Ed Jovanovski, Jeremy Roenick, Owen Nolan and Georges Laraque to complement promising young players.
But the strategy blew up when they started the season 2-8, and the playoffs have been out of sight for quite some time for the worst team in the Western Conference. Jovanovski has missed 13 straight games with a groin injury, Roenick's playing time has steadily decreased and Laraque was traded.
And while Phoenix looks to the future, the Wild can't wait for the playoffs.
Before the game, the scoreboard read, "We don't just want a playoff spot, we want the division," eliciting loud cheers from the fans.
With eight of their final nine games at home, the Wild have designs on the franchise's first division title.
Notes: Phoenix RW Owen Nolan left the game in the second period with a leg injury and didn't return. ... Minnesota captain Mark Parrish took a slap shot off his right arm on a power play in the second period and didn't come back. ... University of Minnesota player Blake Wheeler, a highly regarded prospect in the Phoenix organization, watched the game from the press box.