Mackie Samoskevich also scored for the Panthers (39-38-4), who have won their past two. Tarasov made 24 saves, stopping all 13 shots he faced in the third.
“I was just trying to make saves. That was a bit more action than there was in the first two periods,” Tarasov said. “I’m just happy. We’re finishing strong, scored a big goal at the end. The last few games we have played at home, we cannot give up. We cannot be soft in our building.”
Matthew Robertson and Gabe Perreault scored for the Rangers (33-39-9), who have lost three straight.
Both teams have been eliminated from Stanley Cup Playoff contention.
“I thought we had our moments,” New York coach Mike Sullivan said. “The third period, the second half of the game, I thought we carried the play. It was a struggle to find the back of the net. We had some really good looks in the third period. Give Florida credit, they were opportunistic. The chances they had, they buried.
“(Quick) played well for us. This was a celebration for him. As we talked about after the game, he is an inspiration to all of us.”
Reinhardt gave Florida a 1-0 lead at 9:35 of the first period. He charged the net and knocked in a rebound after Quick stopped Tobias Bjornfot on the rush.
Reinhardt, who was claimed off waivers from the Vegas Golden Knights on March 6, has four goals in a three-game goal streak.
“This is a new chapter in my career and there is a little success happening right now, so I’m just trying to run with it,” the forward said. “You want to make a good impression when you come in, play the right way and be in the lineup next year.”