Kane, whose 64 points are tied for the NHL lead, was injured at 7:49 of the first period when he was cross-checked by Panthers defenseman Alex Petrovic, lost his balance and fell hard into the boards in the Florida end.
Kane's left shoulder and arm appeared to take the brunt of the impact. The Blackhawks called it an upper-body injury.
"It looks like he might miss some time, but we'll know the extent of it [Wednesday]," Chicago coach Joel Quenneville said. "He's having one of those years that are really noticeable, but you've still got to stick with it. You've got to go with what you've got and contribute as best you can. Playing the right way will be emphasized as we go along."
Kane leads the Blackhawks with 27 goals and 37 assists in 61 games. Recently, he's been double-shifting at times to help make up for a lack of production from the bottom two lines.
Chicago (36-20-5) went 3-2-3 on an eight-game homestand, the longest in Blackhawks history. The win ended a three-game losing streak (0-2-1)
"We missed [Kane] for the majority of [this] game, and it was one of those where we were good for 40 and hung on there at the end," Quenneville said. "That's a big two points, and certainly, as a group, we've got to make sure that everybody plays the right way, plays tighter and has some responsibility to their games because we've got to play tight and look to play low-scoring games."
Despite blowing a two-goal lead in the third period, Chicago improved to 19-0-0 when leading after two periods. Rookie goalie Scott Darling, who the Blackhawks called up from Rockford of the American Hockey League and signed to a two-year contract through 2016-17 on Sunday, made 34 saves.
"The point was huge," said forward Vincent Trocheck, whose goal at 16:31 of the third was upheld by video review and forced overtime. "The fact we were down 2-0 to a team like that, they're a great team and we didn't have any doubt that we could come back and win that game. The third period showed that. We had a lot of character and came back and tied that game up."
Panthers forward Jussi Jokinen scored at 12:23 of the third to make it 2-1.
Darling had to make a few high-quality saves with time running out in overtime to force the shootout, in which he denied Trocheck and Nick Bjugstad. Chicago got goals from captain Jonathan Toews and left wing Patrick Sharp in the first two rounds of the tiebreaker.
Toews opened the scoring at 9:25 of the first period by scoring on the power play that followed Petrovic's cross-checking penalty on Kane.
Versteeg's 13th goal made it 2-0 at 14:28 of the second. It was his fourth goal in seven games since returning from a broken left hand.
Sharp assisted on Versteeg's goal for his 500th point with the Blackhawks.
Kane's injury dominated the talk inside the Blackhawks locker room.
Versteeg said it will be disappointing if Kane has to miss extended time. He recalled a conversation the two of them had in which Kane expressed disappointment with the start to his season.
"His season probably wasn't going the way he wanted it to go, and we talked about getting him going and getting him on the right foot and hopefully winning him, maybe, a scoring title one day," Versteeg said. "He was well on his way, so I'm sure he's heartbroken right now if it is something [that keeps him out awhile]."
The Blackhawks visit the Panthers on Thursday.