First, he teamed up with Vladimir Tarasenko, passing out on the right, then got the puck back in the middle to make it 1-0 after four minutes.
Then Zibanejad made it 2-1 at the end of the first period after collaborating with Artemi Panarin.
In front of goalie Darcy Kuemper, he made a quick move and lifted the puck in with a backhand.
- I think we came out strong and played at a high pace.
It is important to have a good feeling when we return home.
It wasn't a perfect game but we did a lot of good things," Zibanejad, his ninth game with at least two goals this season, told the NHL.
Club record for Washington's Rasmus Sandin
The New York Rangers have been on a four-game road trip and haven't played at home at Madison Square Garden since March 2.
It was the first period that established victory.
The Rangers won it 3-1 after winning the shots 19-9.
In Washington, Rasmus Sandin was noted for a club record.
He now has eight assists in his first five games for Washington.
The previous record was held by Geoff Courtnall who needed six games to score his eight goals in the 1988-89 season.
Washington played without superstar Alex Ovechkin who was injured (lower body).