Whitney's power-play goal 1:30 into overtime lifted the Hurricanes over the Panthers 4-3 on Sunday.
Florida blew a two-goal lead in the third period and lost for the sixth time in seven games to the Hurricanes. It was the second time Carolina beat Florida on an overtime goal by Whitney.
Carolina, which is close to becoming only the third defending Stanley Cup champion to miss the playoffs the following year, pulled within two points of eighth-place Montreal. The 1970 Montreal Canadiens and the 1996 New Jersey Devils were the other two teams to not qualify for the playoffs the season after winning it all.
"It was a gut-check kind of game, and we responded to it. We got behind, but the important thing is the end result," Whitney said. "It turned out to be a good day for us. We were up to the challenge this time."
The Hurricanes visit Tampa Bay on Tuesday and close with home games against Atlanta and Florida.
The Panthers got two first-period goals from Jozef Stumpel, who set a career high with 23 goals on the season, and led 2-0 after the first period.
But they couldn't hold off Carolina late as Chad LaRose tied the game 3-3 at the 16:35 mark of the third period. That score followed a short-handed goal by Rod Brind'Amour four minutes earlier.
Down 2-0, Carolina got on the scoreboard 2:35 into the second period on a slap shot by Dave Tanabe from above the right circle that went inside the far post past goalie Ed Belfour.
Florida restored the two-goal lead when Chris Gratton tipped in Juraj Kolnik's slap shot from the left point 11:31 into the second period. Jay Bouwmeester got the second assist, the 100th of his career.
But Carolina's special teams keyed its rally, first on Brind'Amour's short-handed goal and then with the help of an unsportsmanlike conduct penalty on Belfour after Bryan Allen's hooking penalty, creating the two-man advantage in overtime.
"We've got to get five or six guys to dive every time you touch them," Panthers captain Olli Jokinen said in reference to Carolina's Eric Staal hitting the ice on Allen's penalty.
"He embellished it as much as he could," said Allen. "It's embarrassing the way they play the game. They're looking for the easy way out, taking dives and looking for the cheesy call."
For a moment, it looked like overtime might not even happen as LaRose's goal was reviewed by the league to make sure his stick wasn't above the crossbar. But after some discussion, the goal stood.
"I never had a doubt (about the goal) until (the refs) started to take a look at it and then I got a little nervous, but the guys on the bench were telling me it was a goal all the way," LaRose said. "It was nice to get one in that situation with so much on the line."