It was a nice reward for the team after it picked up the pace just past the midway point of the game. The Wild started the second period by going more than seven minutes without as much as a shot on goal, and had just six shots on Rangers goaltender Jeremy Brodeur when New York's Ville Meskanen made it 3-0 at 11:04 of the second.
But following back-to-back penalties on the Rangers, Mason Shaw dished down low to Sokolov, who wheeled around the net and snuck the puck between Brodeur and the post at 19:44.
The Wild carried that momentum into the third, drawing within a goal on a snap shot by Greenway from the slot following a fantastic pass by Gerry Fitzgerald, drawing the defenseman to him in a 2-on-1 rush and somehow threading a pass to Greenway all by himself.
It was Greenway's first goal of the tournament and third point after he assisted on two goals Friday against Detroit. It was also Fitzgerald's third point of the weekend.
Sokolov now has two goals in the tournament, both of which have come with the man advantage.
Fitzgerald nearly tied the game on a one-timer from the left circle with under a minute remaining in regulation, seconds before Ryan Lindgren iced the game for the Rangers with an empty-net goal.
Combined with Detroit's win over the Dallas Stars on Saturday, all four teams in the Ted Lindsay Division enter the final day of round-robin play with a 1-1 record. Following an off day on Sunday, the Wild will face the Stars at 2:30 p.m. CT on Monday, while the Rangers will play the Red Wings.
If the Wild and Red Wings each score victories, Minnesota will play in the tournament championship game on Tuesday evening. Wins by Minnesota and New York on Monday would put the Wild in the third-place game.
A loss by Minnesota would relegate it to a Tuesday afternoon game for either fifth or seventh place.
More from Traverse City:
- Shaw comes full circle in Traverse City return
- Army ready for another shot as head coach
- Greenway, Kahkonen help Wild to win over Red Wings