The Panthers had not won two straight games since March of last season.
"I think this team is starting to become more consistent," Bure said. "We have been getting some great goaltending the last two days."
Bure set up Florida's first goal just 63 seconds into the contest when he poke-checked the puck from defenceman Kenny Jonsson at centre ice and skated down the right side, passing it to Kristian Huselius along the right boards.
Huselius skated to the right faceoff circle and wristed the puck past goaltender Garth Snow for his 14th goal of the season -- the most among NHL rookies.
With 5:24 left in the first period, Bure again took the puck at centre ice and fed ahead to Kevyn Adams, who skated down the right side before making a cross-ice pass to Niklas Hagman in the left circle.
Hagman took a wrist shot that beat Snow for his third goal of the season and second in two nights.
"Kristian's goal gave us the momentum and Niklas helped us build our confidence," Bure said.
After Brad Isbister closed the gap to 2-1 with 9:27 left in the game, Bure added an empty-netter with 11 seconds to play for his ninth of the season.
He has five points in his last two games since returning to the lineup Wednesday after missing three weeks with a concussion.
"It was one of the easiest goals I have scored," Bure said.
"Olli (Jokinen) did the tough job of getting the puck away from them and getting it to me. All I had to do is skate and shoot."
Isbister stood at the left side of the crease and banged in a rebound off a shot by defenceman Adrian Aucoin that hit Luongo in the pads.
It was Isbister's eighth goal and second in the last four games.
It was Luongo's second win in five meetings with his former club since he was acquired by Florida on June 24, 2000. He is 1-2-0 this season against the Islanders.
The victory was the 542nd in the regular season for coach Mike Keenan, tying him for fourth all time with Billy Reay.
"It's a great honour," Keenan said.
"Obviously, I have had some tremendous teams to be in that category with Hall-of-Fame coaches."
Luongo is just 2-6-0 in his last eight games since Nov. 24, the same day the Islanders won their last game at home. They are 0-3-3 since.
"It was probaly one of our best games in quite a while," New York captain Michael Peca said.
"We're going through some tough times, but we should be a lot more satisfied in the way we played tonight."