The Wild have 86 points, two ahead of Colorado and Calgary and four in front of Vancouver, which holds the final playoff spot in the Western Conference.
Minnesota, which had lost nine of 13, killed off a pair of early penalties, then scored on Burns' goal at 8:54 on the its first power play. The Wild had not scored in their previous 18 power-play chances at home.
Joe Sakic tied the score on a power play at 4:51 of the second period, but Radivojevic tipped in a Burns pass at 9:42 of the period for the eventual game-winner.
Colorado entered the game with the worst road power play in the league at 11.2 percent. The Avs converted only one of six chances, but missed on a crucial advantage with six minutes remaining in the third.
Minnesota has killed 10-of-11 power plays the last two games - its first back-to-back home victories in regulation since Dec. 18 and 20.
Jose Theodore stopped 26 shots, including a brilliant sliding save of Pierre-Marc Bouchard's backhand that kept the Avs in the game with eight minutes to play.
Colorado had plenty of chances with Theodore pulled for an extra attacker in the final minutes, but Minnesota's Stephane Veilleux scored from the opposite circle with 6.4 seconds remaining.
The Avs lost for just the third time in their last 11 games.
Notes: Avs center Peter Forsberg was back in the lineup after missing four games with a groin injury. ... Wild forward Derek Boogaard returned to action for the first time since Jan. 22 at Calgary. He missed 23 games with a bulging disc. ... Colorado defenseman Jordan Leopold, who played college hockey at the University of Minnesota, missed his fourth straight game with concussion-like symptoms despite practicing at full speed on Sunday.