After resuming on 163-4, still only 73 runs in front, the hosts' initial job was simply to save the game.
Captain Ryan ten Doeschate's 109 helped to do that before Napier took over.
He hit 124, only his seventh first-class century, including three late sixes in one over, as Essex declared on 470-8 before hands were shaken.
David Masters was still there at the end on 47, while Tom Westley earlier weighed in with 44.
Essex's haul of 11 points from the match takes them back to the top of Division Two by one point from Kent, while Sussex, although still unbeaten in 10 games, are in sixth, now 41 points off top spot.
Colchester-born Graham Napier made an emotional century on his farewell appearance at Castle Park as Essex batted out the day to draw with Sussex.