Knockaert scored from close range after an assist from Jose Izquierdo.
Steve Cook equalized for Bournemouth with a looping header in the 33rd minute from the center of the box before Glenn Murray put the Seagulls ahead once more at the Amex Stadium three minutes after the interval. Brighton forward Izquierdo again produced the assist in an unselfish display.
Callum Wilson grabbed a point for Bournemouth with around 10 minutes to go, sending his shot into the bottom right corner for his second goal in three games.
Bournemouth goalkeeper Asmir Begovic made several key saves in the game and stopped Izquierdo getting on the score sheet with an instinctive point-blank stop.
Midtable Brighton has 23 points from 22 games, Bournemouth has 21 from 22.