It was an upsetting result for last season's Turkish champions.
Kasimpasa forward Umut Bozok scored the equalizer in the 82nd minute, making a close range finish after Eren Elmali's low cross from left.
Besiktas has underperformed in their last five league matches, with four losses and a draw.
They are in the ninth position with 21 points in 15 league matches.
Kasimpasa have 11 points and are in the relegation zone.