New York outshot the Capitals 20-10 in the opening frame, but had just the one goal to show for it after an apparent Zibanejad power play goal was wiped off the board following a Washington challenge for offside.
Despite that, Henrik Lundqvist said he felt the team's performance in the first period set the tone for the rest of the afternoon.
"We had a really strong first period," said Lundqvist, who finished with 31 saves for his 27th win of the season. "We could have been up a couple goals. It's a little tricky. They're coming off a bye week and playing back-to-back … it's tough to get your game going the first couple games. I felt like we took advantage of that the first half of the game. They picked up their game a little bit."
Pick it up they did, as Washington controlled the play throughout the middle frame, and eventually tied it on a power play goal by Alex Ovechkin with 2:36 remaining in a period in which the Capitals outshot New York 11-4.
Lundqvist said the team's confidence did not waver after the strong start or the dip in the middle, and that self-belief paid off with Zuccarello's winner.
"A big play by that line and that was the difference," Lundqvist said. "It could have gone either way, but after going into the third period feeling confident and believing we could win this one - I think that's huge."
Head coach Alain Vigneault said he was pleased with the way his team performed in all three zones, and that while there were dips, his team ultimately found a way to take two points from the one of the League's best.
"In this league with the fine line that separates every team, you have to find different ways, and that's what we did tonight," Vigneault said. "We went in there in the third more on our toes. We had to check real well and we had to get some saves, and we did. That's a real strong hockey team. They're not in first place in the league for nothing … We beat a real good team tonight.