Garland's power-play goal gave Arizona a 3-2 lead at 3:57 of the third period. Pitlick scored on a deflection to make it 4-2 at 6:15, then scored into an empty net for the 5-2 final at 19:13.
The Coyotes won despite not scoring in the first period for a 10th consecutive game. They've allowed 13 goals in the first since Garland scored 21 seconds into a 5-4 overtime loss to the St. Louis Blues on Feb. 13.
"We haven't been very happy with our starts, and that's been an issue of late, so we had to buckle down and we knew it," Coyotes forward Lawson Crouse said. "We weren't happy, but after that we came out and played a great hockey game. … We've got to keep playing this way, with the same intensity and the same compete level."
Dumba poked the puck over the goal line to give the Wild a 1-0 lead at 14:20 of the first, and Greenway's wrist shot from the top of the right circle made it 2-0 at 15:12.
Minnesota has scored at least two goals in the first period in seven of its past 10 games.
"But they seemed to have more legs than we did," Evason said. "We just didn't have enough to get it done."
Crouse cut it to 2-1 at 1:25 of the second period with his first goal in 23 games, last scoring in a regular-season game March 4, 2020, against the Vancouver Canucks. He scored two goals in nine postseason games last season.
"I think I felt 1,000 pounds lighter there (after scoring)," Crouse said. "… We just wanted to come out and attack, attack, attack, and we did. At that point we just had to lock it in."