Eric Staal had a goal and an assist, and Sergei Bobrovsky made 23 saves for Florida (16-18-4), which has lost two straight and five of six.
"I thought we battled hard tonight," Panthers forward Sam Bennett said. "We kept trying to push back, and then they were able to get that extra one to keep us two behind. So we had a good push, but it wasn't enough."
Zibanejad gave the Rangers a 1-0 lead at 14:36 of the first period. With the teams skating at 4-on-4, he drove to the slot and lost control of the puck, which slid past Bobrovsky just as a penalty to Trocheck expired for a power-play goal.
"We trust each other," Zibanejad said. "We trust that we can be a good power play and that we are a good power play and that the goals will come. And they did so today, so that was nice."