It was the eighth time in nine games the Wild allowed the first goal, but they got it back 35 seconds later.
Greenway, who was recalled from Iowa of the American Hockey League on Sunday after he had a hat trick Saturday in one of two games after being sent down, banged in the rebound of his own shot to tie it 1-1 at 7:52.
"It would have been a lot nicer to get a win with it," Greenway said. "I really wanted to get pucks to the net, go to the net, just like I did a couple of days ago in Iowa. It worked out for me. I might keep doing it."
Minnesota was an NHL-best 5-1-1 when the opponent scores first, but Jake Virtanen put Vancouver ahead 2-1 at 5:15 of the second period when he scored on the power play with a shot from the high slot through a screen on the rush.
"You keep doing that too often, I told them, it's going to happen," Wild coach Bruce Boudreau said. "Nobody is able to come back all the time if you're going to start that slow."