Kane stuffed home a rolling puck in the crease that came off the stick of Bryan Bickell, who was redirecting Niklas Hjalmarsson's shot from the point. The goal tied the score at 2-2 with under two minutes remaining in the second and defined the level of grit the Blackhawks played with to take a 3-1 series lead.
Kane, who hadn't scored since the 3-1 loss in Game 3 of the Detroit series 17 days ago, went into the corner after a rebound and made the pass out to Hjalmarsson. Playing through pain tonight after blocking a shot in Game 3, the Swede had two assists and was among the leaders in ice time, picking up some of the minutes abdicated by Duncan Keith, who was serving a one-game suspension.
Exuding patience at the point, Hjalmarsson waited after receiving the pass from Kane and fired, connecting with Bickell's stick in front of the net. The puck trickled through Jonathan Quick's pads and appeared to be going in before Kane tapped it home for good measure.
The goal finally brought about more confidence from Kane, who led the Blackhawks in shots in Game 4 with seven.
The Blackhawks' forecheck continued to get stronger as the game went along, and an outlet pass from Johnny Oduya early in the third allowed Chicago to capitalize on its momentum.
Michal Handzus took the stretch pass from Oduya before feeding a saucer pass to Marian Hossa, who buried the one-timer and the Kings' home playoff streak in one fell swoop.
Los Angeles had won 15 straight at home in the postseason and had won 22 straight home games when scoring the first goal, as it did in Game 4.
Chicago was 2-3 this postseason when its opponent scored first, but for the second time in this series, it rallied from an early deficit to come back and win.
The 'Hawks had their star players step up when needed tonight, with the top line of Jonathan Toews, Kane and Bickell doing most of the damage. Bickell added his eighth goal of the postseason while Toews, who was held off the scoresheet, moved the puck efficiently and kept the play alive that led to the Kane goal.
Hossa added his seventh marker of the postseason with the go-ahead goal just 70 seconds into the third period, earning his 10th career playoff game-winner in the process.
Brent Seabrook, the Game 7 hero against Detroit, led the 'Hawks in ice time with 26:20 while eating some of Keith's minutes.
Chicago will have a chance to close out the Kings on home ice back at the United Center on Saturday in Game 5.
Los Angeles is a dismal 1-7 on the road this postseason and will need to play with an unmatched desperation in Game 5 to have a chance at bringing the series back to the west.