Vincent Trocheck and Mike Hoffman scored for the Panthers (1-3-3), who have had a lead in every game this season but have one win.
Florida is the only team in the NHL without a regulation or overtime win; it defeated the Washington Capitals 6-5 in a shootout on Oct. 17 for its lone victory.
"It's hard to take positives out of that," defenseman Aaron Ekblad said. "For some reason, we have a tough time holding onto leads. Once we get that lead, we aren't playing aggressive enough."
Zibanejad's second of the game came on the power play at 16:08 of the second to give the Rangers a 3-1 lead. He has five goals in his past five games.
"He's a complete player," Rangers coach David Quinn said. "I knew he was a good player before I got this job; I didn't know he was this good. This is a guy who does a little bit of everything. He's got skill, he's tough he can skate. ... We are lucky to have him."