Luongo, who had missed the previous six games because of a hand injury, made 39 saves.
"Not great," Luongo said of his performance. "My timing was a little bit off. I only had one full practice. I wasn't as sharp as I would have liked to have been. I knew what I was getting into. I didn't impact much, but (I) knew I wanted to play tonight."
Shattenkirk scored the game-winner on a 2-on-1 after getting a pass from Nash.
"The ice was a little choppy at the end of the game there, so I just wanted to make sure I settled it down and got my head up," Shattenkirk said. "I figured at that point I know he's a pretty aggressive goalie, so I figured I might have that far side."
Vincent Trocheck sent the game to overtime when he scored with 1:04 remaining in the third period. Colton Sceviour, who returned after missing five games because of an upper-body injury, scored twice for Florida (4-7-2), and Keith Yandle had a goal.
The Panthers ended their five-game homestand 1-2-2. They start a three-game road trip Tuesday against the Carolina Hurricanes.
"We're looking forward to (the road trip)," Panthers coach Bob Boughner said. "Obviously, there's been some frustrations with the last few. Sometimes the road is a good thing."
The Rangers twice had a one-goal lead in the third period.
Grabner gave the Rangers a 3-2 lead at 5:18 of the third period before Yandle tied it at 8:45 with a wrist shot that deflected in off Holden.