McDavid put Edmonton ahead 2-1 on the power play with 57 seconds left in the first, pulling the puck in quickly to shoot between the legs of defenseman Chris Tanev from the top of the left circle on the rush.
"There's probably one guy that can do that," Sutter said of McDavid, who has six goals and three assists during a six-game point streak and 37 points (16 goals, 21 assists) in his past 22 games.
Granlund scored unassisted at 9:52 of the second, quickly shooting over Koskinen's glove from the bottom of the left hash marks to tie it 2-2.
Ben Hutton scored on a power play with 1:06 left in the second, but the goal was overturned after Edmonton coach Ken Hitchcock successfully challenged that Jake Virtanen was offside on the play.
"Huge break on that offside," McDavid said. "At least we were able to take advantage of it."
Koskinen got across on a backdoor pass to glove Bo Horvat's high one-timer five minutes into the third period, made the save on Virtanen on a partial breakway with 19 seconds left, stopped Horvat on a breakaway in overtime, and was 5-for-5 in the shootout.
"Overtime was really exciting," Hitchcock said. "I thought we'd score for sure twice, and then next thing I know, I couldn't believe they didn't score."