Resuming on 116-0, a lead of 321, Kent lost Daniel Bell-Drummond (90) and Sean Dickson (74) in the first session.
But Joe Denly made an unbeaten 71 off 49 balls as Kent raced to a declaration on 298-2, a lead of 503 runs.
Matt Coles took two wickets as Sussex slumped to 8-3, while Denly also accounted for two dismissals to leave the visitors on 182-6 at stumps.
Stiaan van Zyl made 78 from 134 balls and added 82 for the fifth wicket alongside Michael Burgess (42 not out), but his dismissal off the bowling of Denly ended any realistic hopes Sussex may have had of salvaging a draw.
Kent closed in on victory over Sussex after a dominant performance with bat and ball at Tunbridge Wells.