Jimmy Vesey and Vincent Trocheck also scored, Artemi Panarin had an assist to extend his point streak to six games and Igor Shesterkin made 25 saves for the Rangers (10-4-1).
Timothy Liljegren and Fabian Zetterlund scored, and Mackenzie Blackwood made 32 saves for San Jose (5-10-3), which has lost four of six (2-3-1) since a three-game winning streak from Oct. 28-31.
The Sharks took a 1-0 lead on Liljegren's goal at 2:51 of the first period. His shot from the point deflected off Vesey high in the zone and sailed into the net, going over both Sam Carrick and Carl Grundstrom in front.
Zibanejad scored off a rebound on Adam Fox's shot at 11:41 of the second period to tie it 1-1. It was his third goal of the season and first since Oct. 22. Zibanejad had three turnovers that led to goals in the Rangers' 6-3 loss to the Winnipeg Jets on Tuesday.
Vesey made it 2-1 at 13:15 of the second. He followed his pass to the net, got the puck back after it hit off Carrick in front and scored with a backhand from the slot.
Fox had a goal taken off the board at 14:32 because of a successful coach's challenge for goalie interference. Vincent Trocheck was ruled to have knocked Blackwood's stick out of his hands as he going to the front of the net, preventing the goalie from playing his position on Fox's shot.
Trocheck got the goal back at 16:21, when he finished a pretty play from Artemi Panarin to make it 3-1.
Panarin hesitated with the puck high in the zone, drawing two defenders to him. Trocheck slipped behind them through the right circle. Panarin found him and Trocheck redirected the pass over Blackwood's glove.
Zetterlund cut the Rangers lead to 3-2 at 19:33 of the third period, scoring a 6-on-4 power-play goal from the front of the net.
