Rangers won the game 6-4 and it wasn't just Zibanejad who managed to scrape together four points - Artemi Panarin had a goal and three assists.
Both of Zibanejad's goals came on the power play.
Panarin and Zibanejad not only impressed in the night's meeting, but also lead the club's scoring so far - Zibanejad with eight points including four goals in total and Panarin with ten points including two goals.
- Last year was a good year for them (Zibanejad and Panarin), but the playoffs were a bit of a disappointment.
They're coming back now, ready to play really well and be a really good team, really good players.
They are both star players but now come in with a boosted sense of self.
Both are playing incredibly well, says Rangers coach Gerard Gallant after the match.
Despite the win and the efforts of the stars, however, Gallant was not completely satisfied and thought that they conceded too many goals.
- I think we played well, but at least two (of Anaheim's) goals should not have gone in.
But excluding the two goals, we played really well, says Gallant.
Anaheim's John Gibson allowed five of 34 shots before being substituted after the second period.
Substitute Anthony Stolarz allowed one more puck in, but made eight saves.
The loss was Anaheim's second in New York in just a few days - the Islanders beat the California team 7-1 last Sunday night.
Rangers, for their part, won the third game out of four played so far.
Isac Lundeström had an assist for Anaheim.