Rask gave the Wild a 2-1 lead at 1:38 of the second period with a wrist shot from the left face-off circle after a cross-ice pass from Jared Spurgeon. It was Spurgeon's 200th NHL assist.
Makar tied it 2-2 with his first goal of the season on a wrist shot from between the circles at 3:31 of the second.
"It's nice and a good relief to get that, but tough to not get the win today," Makar said.
Brandon Saad, who had a goal and assist in a 5-1 win against the Wild on Saturday, scored off the rush at 7:09 of the third to give the Avalanche a 3-2 lead.
Rask tied it 3-3 with a wrist shot from beyond the circles after a pass from Kirill Kaprizov at 12:34.
"It definitely felt good for the confidence," Rask said. "First goal was obviously a real good pass by [Spurgeon] … it was nice to get that one. The second one, I just tried to get it on net, and luckily it went in."
NOTES: The Avalanche were already without defenseman Erik Johnson, who was injured at 9:24 of the first period on Saturday. Bednar said he doesn't expect Johnson to rush back. … The Wild are 3-0 in overtime games this season. … Greenway extended his point streak to four games (one goal, four assists). … Donskoi (three goals, one assist) and Makar (one goal, five assists) also have four-game point streaks.