Kane got his fifth goal in seven games 8:29 into the third by taking a cross-ice pass from Brian Gionta and beating goalie Petr Mrazek with a high wrist shot to the glove side.
The Wings rallied from 2-0 and 3-1 deficits and thought they had tied it late when Frans Nielsen appeared the score, but the whistle had already been blown because goalie Robin Lehner was hurt after being struck in the throat by teammate Zach Bogosian's stick.
Lehner was able to continue after being attended to by the Buffalo training staff.
Kane gave the Sabres a first-period lead by jamming the rebound of his wraparound attempt under Mrazek's arm.
Sam Reinhart made it 2-0 on a power play later in the opening period.
The Wings got on the board at 14:46 of the second period when Henrik Zetterberg threw the puck toward the net from the corner of the rink and it banked in off Lehner's shoulder.
Just 23 seconds later, Buffalo's Jack Eichel skated around Detroit's Thomas Vanek and lifted a high shot past Mrazek.
Before the period was done, the Wings scored again. Dylan Larkin's shot hit teammate Drew Miller in the leg in front of the Buffalo net. The puck landed at Miller's feet, and he snapped a quick shot past Lehner.
Vanek's third-period power-play goal tied it at 3.
NOTES: Detroit D Brendan Smith returned to the lineup after missing 12 games due to a knee injury. ... The Red Wings honored their 1996-97 Stanley Cup team prior to the game.
Sabres: Host Boston on Thursday night to begin a home-and-home set.
Red Wings: Play at Ottawa on Thursday night.