Zibanejad entered the Sabers zone 2-1 and passed to Artemi Panarin, who returned the puck to Zibanejad for a stopwatch from the left circle.
Buffalo’s Tage Thompson forced overtime with 3.6 seconds left in regulation on a left circle wrist shot with the extra forward.
Colin Blackwell and Filip Chytil also scored for the Rangers, who have won two in a row after dropping a pair. Igor Shesterkin made 21 saves.
Rasmus Asplund also scored for Buffalo, who lost one night after ending their 18-game winless streak (0-15-3). Dustin Tokarski made 44 saves.
Chytil gave the Rangers a 2-1 lead at 6:17 of the third period. In a scrum in front of the net, Julien Gauthier pushed the puck towards Chytil, who scored on a wrist shot from the lunge.
The Rangers beat the Sabers 36-10 in the second and third periods.
Asplund, who had missed the last four games with a lower body injury, gave the Sabers a 1-0 lead at 2:06 of the first period when he blocked the puck at home in the ‘a scrum in front.
Blackwell’s ninth goal of the season tied the game 1-1 at 6:40 of the second period. Blackwell hit the crossbar in a two-on-one run, but Ryan Strome got the rebound and passed the cross ice to Blackwell, who scored on a clock from the left circle.
Strome extended his points streak to 11 games (two goals, 14 assists).
The Rangers were 0 for 4 on the power play, while the Sabers were 0 for 1.