Weiss picked up the puck and went in on goal with speed. He made a quick move to his backhand and squeezed the puck through the pads of Hurricanes' netminder Justin Peters.
Jose Theodore stopped 2-of-3 shooters in the shootout and made 26 saves in to record the win.
Wojtek Wolski, who was acquired by the Panthers earlier on Saturday from the New York Rangers, and Tomas Fleischmann scored for Florida, which snapped a four-game losing streak and moved back into a first place tie with the Winnipeg Jets in the Southeast Division.
Justin Falk and Jussi Jokinen scored and Peters made 42 saves in defeat for the Hurricanes, who have dropped three of their last four.