The Oilers (20-34-7) have lost two in a row after winning five of their previous six.
It was the fifth time this season that the Oilers have been shutout at home and eighth time this season they have failed to score in a game.
The game started with a bang as Oilers forward Matt Hendricks checked Wild defenceman Nate Prosser in to the boards in the first minute of play. Prosser was helped to the dressing room and did not return until the second period.
Minnesota got revenge for the hit by taking a 1-0 lead a minute later as Oilers goalie Ben Scrivens was caught out of position as Zach Parise fed the puck in front to Granlund who had an empty net to put his team's first shot of the game into.
Each team only accounted for six first period shots apiece, with Edmonton's best chance coming late in the period when a high bounce flipped off of Kuemper's back and landed in the crease before being sent to safety by Jared Spurgeon.
Kuemper made a big save of his own seven minutes into the second as he was quick to come across and rob Jordan Eberle at the side of the net on the tail end of an Oiler power play.
Minnesota made it 2-0 midway through the second period as Erik Huala fought off Oiler Anton Belov behind the net to send a backhand to a primed and ready Veilleux who blasted a one-timer from the top of the circle past Scrivens for just his second goal of the season.
The Wild took a three-goal lead midway through the third as Charlie Coyle made a nice play to swing out from behind the net and find Heatley in front, who lifted his 12th of the season over a sprawling Scrivens.
The Wild return to the ice on Friday night when they travel to Vancouver to face the Canucks. Edmonton plays the second game of a five-game homestand on Saturday against the Calgary Flames.
Notes: Both teams saw some success before the pause in the NHL schedule as the Oilers were 5-1-1 in their previous seven games, while the Wild were 4-1-2 in their last seven. Edmonton only allowed 12 goals during that seven-game stretch… The Wild have had a great deal of success against Edmonton in recent years, coming into the game having won five of six and 14 of its last 17 versus the Oilers, including seven of their last eight appearances in Edmonton… Minnesota forward Mikko Koivu is reportedly close to returning but remained out with an ankle injury for Thursday's game… Minnesota goaltender Niklas Backstrom returned from an abdominal injury dating back to Jan. 30, but served as the backup to Kuemper… It was Edmonton's only home game in all of February. The Oilers last home date was on Jan. 29 when Scrivens set an NHL record for most saves in a shutout with 59 in a 3-0 victory over the San Jose Sharks… Oiler forward Nail Yakupov took a shot to the leg from teammate Justin Schultz in the third and did not return.