Kulak finished Martin Necas’ crossing pass with a one-timer from the right dot past a sprawling Jesper Wallstedt to cap Colorado's four-goal, comeback rally.
Minnesota blew a three-goal, first-period lead. With Scott Wedgewood pulled for the extra attacker, Nathan MacKinnon tied it 3-3 at 18:37 of the third period with a wrist shot from under the left dot that went top shelf short side over Wallstedt's shoulder to send it to overtime.
The Avalanche will play either the Vegas Golden Knights or Anaheim Ducks in the Western Conference Final. Vegas leads that series, 3-2.
Parker Kelly scored a goal and had an assist, and Necas and Brent Burns each had two assists for the Avalanche, the No. 1 seed from the Central Division and the Western Conference. Mackenzie Blackwood allowed three goals on 13 shots before being replaced at the start of the second period by Wedgewood, who stopped all seven shots in relief.
Nick Foligno scored twice, and Marcus Johansson also scored for the Wild, the No. 3 seed from the Central. Matt Boldy and Nico Sturm each had two assists, and Wallstedt made 30 saves.
Johansson scored to make it 1-0 Minnesota 34 seconds into the first period with a one-timer from the left circle that beat Blackwood's glove far side. Boldy made a move to shake off Colorado forward Brock Nelson in the left corner before sending a backhand pass to Johansson from below the goal line for the play.
Nick Foligno extended it to 2-0 at 11:03 after he snuck around Kulak on the rush and redirected Sturm’s centering pass five-hole. Blackwood appeared to make the save initially, but the puck trickled through.
Michael McCarron appeared to make it 3-0 at 12:25 after the rebound of Kirill Kaprizov’s initial shot ricocheted off the crossbar, caromed off McCarron and got through Blackwood's five-hole. Video review determined the puck was played with his hand, and the goal was overturned.
Nick Foligno scored again to make it 3-0 at 15:56 when he finished another Sturm centering pass at the left side of the net. Sturm made a desperation play, diving to knock his own rebound across the crease to Foligno, who was wide open for the snap shot into the open net.
Kelly cut it to 3-1 at 11:00 of the second period when he deflected Burns’ point shot short side past the left shoulder of Wallstedt. Colorado forward Joel Kiviranta dug the puck out of a scrum in the left corner and fed it up the boards to Kulak, who sent it point to point to Burns for the shot.
Jack Drury made it 3-2 at 16:27 of the third period after deflecting Devon Toews' point shot in the high slot. Drury won the face-off at the left dot and stationed himself in front of the net, battling until the shot came his way.
