Patrick Kane scored the only goal in the tiebreaker as Chicago won for the third time in four games and stopped Tampa Bay's six-game winning streak. The Blackhawks had lost their last five games against the Lightning, with four of the defeats coming in a shootout or overtime.
Brad Richards and Marcus Kruger scored in regulation for the Blackhawks, who have won consecutive home games after dropping three in a row at the United Center.
Bishop had 37 saves for the Lightning, who were coming off a 4-3 shootout victory at Detroit on Sunday. Cedric Paquette scored in the first, and Kucherov had Tampa Bay's other goal in the third.
The tight matchup of contenders got more physical as the game wore on, and it took a toll on the players.
Tampa Bay center Tyler Johnson, who leads the team with 13 assists, departed after he was cross-checked in the back by defenseman Brent Seabrook in the third. Blackhawks defenseman Johnny Oduya also left in the final period with an apparent right leg injury.
Kruger gave the Blackhawks a 2-1 lead when he tipped Niklas Hjalmarsson's long slap shot by Bishop 1:18 into the third. But the Lightning tied it at 2 when Stamkos made a nice pass through the crease to set up Kucherov's sixth goal at 9:53.
Bishop stopped Jonathan Toews on a 4-on-4 breakaway with 8:20 left in regulation, and Crawford made a pair of saves on Callahan in overtime.
The Blackhawks put a ton of pressure on Bishop right from the start, and the 6-foot-7 goalie kept the Lightning in the game with a series of outstanding saves. It was reminiscent of his previous start in Chicago, when he had 37 stops to help Tampa Bay rally for a 3-2 shootout victory last October.
Toews got a great in-close look about 7 1/2 minutes into the game, but Bishop made an impressive right pad save. He also stopped Kris Versteeg and Richards in rapid succession with about 3 minutes left in the period.
Chicago outshot Tampa Bay 19-6 in the first, but the Lightning's second short-handed goal of the season was enough for a 1-0 lead at the first intermission. Paquette finished off a slow-developing 2-on-1 with Ondrej Palat, sliding a shot through Crawford's legs for his fourth goal at 4:35.
Bishop kept up his solid play in the second, and got some help from defenseman Valtteri Filppula when the Blackhawks had a successful odd-man rush. Kane's shot off a pass from Versteeg got behind Bishop and was sitting right on the goal line when Filppula swept it away.
The crowd of 21,345 groaned as replays showed how close Chicago was to the tying score, but Richards put the Blackhawks on the board when he followed his own shot for his third goal at 9:13. Richards has six points in his last seven games after a slow start in his first season with Chicago.
NOTES: The game marked exactly one year since Stamkos broke his right leg in a 3-0 loss at Boston. Stamkos leads the team with 10 goals this season. ... It was the fourth short-handed goal allowed by the Blackhawks in 16 games this season. ... Tampa Bay scratched C Alex Killorn, RW Brett Connolly and D Mark Barberio. ... Blackhawks D Michal Rozsival played for the first time since a 3-2 loss at Toronto on Nov. 1. D David Rundblad joined injured forwards Patrick Sharp and Daniel Carcillo on the scratch list. ... The Blackhawks warmed up in camouflage jerseys in honor of Veterans Day. The jerseys will be autographed and then auctioned online, with proceeds going to the USO of Illinois. ... It was the 500th career game for Toews.