Athanasiou tapped in a cross-crease pass from Tyler Johnson on a 2-on-1 rush for the game-winner.
"I think we just stuck with it, stuck with it together," Athanasiou said. "We kind of just chipped away and didn't try to make any crazy plays. We just kind of put our nose down, didn't say much and just worked and found a way."
Sam Lafferty cut it to 3-2 at 10:49 of the third period, scoring glove side on Mads Sogaard on a short-handed breakaway before Patrick Kane tied it 3-3 at 16:55, shooting on a 2-on-1 rush and beating Sogaard blocker side with a wrist shot.
"I just thought we never really gave up," Kane said. "Even down 3-1, we had a good attitude on the bench. The first period was good, second period was not, and then the third, obviously being down 3-1 you don't have much life. But you get a short-handed breakaway and then all of a sudden it's 3-2 out of nowhere, and you feel like you have a chance."