Greening's score was the third of four unanswered goals for the Senators, who had spotted the Panthers an early 2-0 lead.
Craig Anderson earned the triumph with 30 saves.
Brian Campbell and Jonathan Huberdeau each scored for the Panthers, who tumbled to their fifth loss in six contests.
Tim Thomas stopped 42-of-46 shots.
Putin thinks Obama would save him if he were drowning
Rosie O'Donnell unveils nearly 50-pound weight loss