The Avalanche also tied a team record with 11 wins in a month, first accomplished in January 2004.
Budaj went 10-0-2 in March, tying the franchise record for wins in any month set by Daniel Bouchard with the Quebec Nordiques in February 1981 and breaking the March mark of nine set by Jocelyn Thibault in 1995 and tied by Patrick Roy in 2000 and '03.
Colorado is five points behind Calgary for the last Western Conference playoff spot with four games remaining. The Flames play at Vancouver Saturday night and host Colorado on Tuesday night.
Minnesota, in a close race with Vancouver for the Northwest Division title, lost its third straight following a franchise-record nine-game winning streak.
The Avs quickly found themselves in a hole when Marian Gaborik's wrist shot from the left circle on the power play gave Minnesota a 1-0 lead just 81 seconds into the game.
Colorado scored both of its goals on power plays in the second period. John-Michael Liles tapped the puck past John Harding, then rookie Paul Stastny put the Avs ahead when he flipped a rebound into the net for his 26th goal after Milan Hejduk's shot hit the crossbar.
The Avs weathered a 40-second five-on-three disadvantage in the third period after Kurt Sauer went to the penalty box for holding while Tyler Arnason was out for hooking. Brett Clark threw his body in front of a shot during the five-on-three skate and limped off the ice. The Wild only had two shots on goal during the entire power play.
The Avalanche have made the playoffs every year since 1993-94, two years before the franchise moved from Quebec City. The only player left from that team is captain Joe Sakic.
Once the franchise relocated in Denver, Colorado enjoyed a decade of dominance before the NHL landscape changed 18 months ago, forcing Peter Forsberg, Adam Foote and Paul Kariya out of town. The exodus of veterans continued last summer with the departures of Rob Blake, Dan Hinote and Alex Tanguay, more victims of the salary cap designed to resuscitate the league.
Unable to just outspend other teams and assemble an abundance of all-star talent as it did in winning the Stanley Cup in 1996 and 2001, the Avalanche turned to a youth movement. After some growing pains, the Avs rebounded behind Stastny, who set a rookie record by scoring in 20 straight games from Feb. 3-March 17.
But it might just prove too little, too late. The Flames could wrap up the eighth playoff spot with a win over Colorado on Tuesday night.
Notes: Minnesota had earned a point in nine straight road games, going 7-0-2. ... Stastny ranks third on the Avalanche in all three scoring categories with 26 goals, 46 assists and 72 points.