With Buffalo holding a one-goal lead, Carolina tied the game on the power play as Semin's shot from the left point hit off a Sabres and went in at 11:48.
Just under two minutes later, the Hurricanes took the lead when Tlusty's wrister from the right circle went through a screen and into the net for his 12th of the year.
Nathan Gerber got the puck into an empty net with just 0.4 seconds showing on the clock to cap the scoring.
Ennis was awarded a penalty shot halfway through the first period when he was slashed by Tlusty on a breakaway and he buried his chance, wristing the puck into the left corner of the net for his 17th of the season.
The Hurricanes tied the game three minutes later, when Skinner made a nifty move in the deep right corner to get around a defender and whipped it home for his 26th of the season.
The second period stayed scoreless despite Carolina throwing 22 shots on net, while Buffalo managed just four in the frame.
Buffalo took a 2-1 lead at 8:43 of the third when Cory Conacher's wraparound from the right side hit off some skates and went to the left where Stafford slammed it home.