Jonathan Toews set up Kane's 12th goal when he forced Anders Nilsson to make a left pad save. The rebound went right to the reigning NHL MVP, who knocked it into the open side of net before Nilsson could recover.
Coach Joel Quenneville was trying to get Kane off the ice before he scored the winning goal .
''The time I wanted him to come was the right time and then he knew that then it was a little too late, that he had to stay,'' Quenneville said. ''I give him credit. He knows the game.''
The Central Division-leading Blackhawks had dropped three in a row at home and five of six overall. Kane also had two assists against his hometown team, and Corey Crawford made 17 stops in Chicago's 10th consecutive victory against Buffalo.
''Nothing better than beating Buffalo, right?'' a grinning Kane said as he addressed the crowd after the game.
Buffalo dropped to 3-9 in overtime and shootouts.
''Too many overtime losses this year,'' Eichel said. ''It's painful.''
The game was tied at 2 when O'Reilly found Eichel for a one-timer from the left circle at 1:10 of the third. It was Buffalo's second power-play goal in three opportunities and Eichel's eighth goal in 17 games this season.
The Sabres then kept the action away from Nilsson for much of the third. The Blackhawks finally broke through when Kane got a backhander to the net and Anisimov knocked in the rebound for his team-best 18th goal with 2:04 remaining in regulation.
''He's so skilled and when he gets those chances in front, he's not going to miss them too often,'' Kane said. ''He's patient, he's skilled and he knows where to put the puck.''
Buffalo also jumped in front in each of the first two periods, only to have Chicago rally each time.
''There is a lot of disappointment giving up that game with the opportunity to win,'' Sabres coach Dan Bylsma said.
Marcus Foligno intercepted a clearing attempt by Chicago defenseman Brent Seabrook in the first and beat Crawford on the glove side for his sixth of the season at 7:21. But Ryan Hartman responded for the Blackhawks, splitting Okposo and Sabres defenseman Taylor Fedun before sending a hard wrist shot over Nilsson's glove at 16:20.
Chicago outshot Buffalo 20-6 in the first, but Hartman's seventh of the season was all it could manage against Nilsson.
The teams exchanged goals again 18 seconds apart in the second. After Chicago was whistled for too many men on the ice, Okposo stuffed one home from the side of the net for his team-best 12th goal. Anisimov then sent a wrist shot over Nilsson's glove for his team-best 17th of the season, tying it at 2 with 1:32 remaining in the period.
NOTES: Blackhawks D Duncan Keith got his 400th career assist on Anisimov's second goal. ... O'Reilly had an appendectomy during the NHL's holiday break and missed four games. D Josh Gorges also returned to Buffalo's lineup after he missed Tuesday's 4-1 victory against the New York Rangers with a hip injury, but F William Carrier was scratched with an illness. ... Blackhawks F Marian Hossa returned after missing five games with an upper-body injury. ... Blackhawks D Brian Campbell was a healthy scratch. ... Sabres C Zemgus Girgensons turned 23 on Thursday.
Sabres: Host Winnipeg on Saturday afternoon.
Blackhawks: Host Carolina on Friday night.
Jay Cohen can be reached at http://www.twitter.com/jcohenap
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