Trailing 2-0 entering the third period, Tomas Fleischmann scored with 6 minutes remaining and newly acquired Wojtek Wolski -- obtained earlier Saturday from the New York Rangers -- netted the equalizer 4 minutes later.
After a scoreless overtime, the game moved to a shootout where Weiss eluded a poke-check by Hurricanes goalie Justin Peters and found the net for the game-winner.
Jose Theodore turned aside 26 shots as well as 2-of-3 in the tiebreaker to earn the win.
The Panthers snapped a four-game losing streak and bypassed the Winnipeg Jets for first place in the Southeast Division.
Peters ended with 42 saves.
Jussi Jokinen and Justin Falk scored for Carolina.
Boston schools pull out free condoms over wrapping complaints
NBC reportedly holds celebs hostage to Jimmy Fallon's show