Kaepernick -- starting in place of the injured Alex Smith -- went 16-for-23 through the air for 243 yards, guiding the 49ers to scores on each of their first four possessions.
The 49ers (7-2-1) made a game-time decision to hold Smith out while he continues to recover from a concussion.
Chicago managed just 151 total yards of offense as linebacker Aldon Smith recorded 4 1/2 sacks and the 49ers' defense intercepted Bears quarterback Jason Campbell twice.
San Francisco head Coach Jim Harbaugh returned from last week's procedure to correct an irregular heartbeat to guide his squad in Monday's game.
Campbell was also playing in place of a concussed starter -- Jay Cutler, who sustained the injury in Chicago's loss to Houston last week. He managed to complete just 14-for-22 passes for 107 yards, a touchdown and the two picks-offs for the Bears (7-3).
The setback was the second straight for Chicago, which fell into a tie with the Green Bay Packers for first place in the NFC Central.