Kane broke a 3-3 tie in the second period with a wrist shot off an assist by Jonathan Toews and then knocked an insurance goal into the empty San Jose net in the closing minute of the third period.
Brandon Saad, Andrew Shaw and Marcus Kruger scored in the first period, which ended in a 3-3 deadlock.
The win was the second in a row for the Blackhawks. San Jose lost its third consecutive game after opening the season with seven wins in a row.
Corey Crawford faced 33 shots and allowed three to hit the back of the net.
Chicago racked up 27 penalty minutes in the game to 23 for San Jose. A sizable fight at 8:48 of the second period churned up a 10-minute misconduct penalty for Chicago's Duncan Keith. San Jose's Andrew DesJardines was slapped with a 10-minute match penalty in the fracas.