Kane scored twice and added two assists Thursday as the Jets pounded the Panthers to move two points behind Florida for the Southeast Division lead, and one point ahead of Washington in the East for the final playoff spot.
"It was great to be able to prove to everybody that we're here to play and we have that playoff mindset going into the next 16 games here," Kane said.
"[Florida is] a team that we're behind and this could very well be the difference in us being in the playoffs or not being in the playoffs so it was a big game for us."
Ondrej Pavelec made 33 saves to earn his fourth shutout this season for Winnipeg, while Kyle Wellwood and Blake Wheeler each had a goal and an assist. Jim Slater, Bryan Little and Nik Antropov also scored.
"Everybody knows that it was a huge game for us, especially against Florida," said Pavelec, who got his 10th career shutout. "They play really well against us so [it was] a big game for us. Like I said, we learned from the last game [a 5-3 loss to Edmonton], especially in the third period.
"We didn't make mistakes like we did before and it was a great win for us."
Jose Theodore made 20 saves on 24 shots in the start for Florida (30-21-12), which had a three-game winning streak snapped. He was pulled after Little's goal made it 4-0 at 4:35 of the third period. Scott Clemmensen made five stops on eight shots in relief.
Florida, third in the Eastern Conference, has three games in hand on the Jets, as does Washington, which next plays Friday at home against New Jersey.
Little's goal came on a rare 5-on-1 break, with Florida defenseman Erik Gudbranson the lone man back.
Wheeler made a nice defensive play to get the puck and bring it up the ice. He then passed to defenseman Randy Jones, who sent it back to him. Wheeler then passed across the net to Little and he popped it in over Theodore.
The fans gave the players a standing ovation for the rare attack.
"I've never seen that before ever," Wheeler said of the 5-on-1. "I was really nervous, actually, because I looked up and I heard the crowd going crazy so I figured, oh, a 2-on-1, 3-on-1, whatever.
"But it was all five guys and I didn't know where to go with the puck. Jonesy seemed like a good option so I gave it to him, hopefully, he was going to give it right back to me."
Kane opening the scoring after he intercepted a clearing attempt by Keaton Ellerby from deep in his zone and quickly fired the puck past Theodore 4:01 into the match.
Slater soon made it 2-0 when he took advantage of a rebound off Mark Stuart's point shot. Theodore was down as the puck bounced to the side and Slater sent a wrist shot into an empty net.
Panthers left wing Tomas Fleischmann had two breakaways in the first period. His first shot went off the crossbar and the second was turned aside by Pavelec.
"We just didn't have the push back at them today," Florida defenseman Ed Jovanovski said.
Florida has won three of five meetings with the Jets this season. They play once more in Florida.
Wellwood's goal began the barrage at 1:49 of the third. After Little's goal, Antropov scored on the power play at 8:06 and then Kane added his second of the game and 26th of the season just 12 seconds later.
Kane is on a career-best eight-game points streak with seven goals and seven assists.
The crowd started chanting "We want perfect" as they cheered for a shutout.
Wheeler netted the game's final goal at 17:58 as Winnipeg tied a franchise record for single-period goals with five in the third.
- Winnipeg is now (4-1-2) in an eight-game homestand.
- Florida had a four-game road-winning streak end.
- Jets defenseman Zach Bogosian was back after missing the past seven games with a wrist injury.
- Panthers' Kris Versteeg missed his second straight game with a lower-body injury.