Paul Grayson produced a late spell of three wickets for 30 runs in 12 overs to help check Sussex's progress in the Frizzell County Championship First Division match.
Tony Cottey scored 107 and Tim Ambrose contributed 88 in a superb fourth-wicket partnership of 178 in 55 overs before the Essex left-arm spinner Grayson struck with his 10th ball to remove Ambrose.
Cottey fell victim in the next over to Jonathan Dakin as Sussex, replying to the visitors' 340, closed on 282 for 8.
Second-placed Sussex were pegged back in the last 80 minutes after being 231 for 3 at one stage on a typically slow Arundel pitch. The hosts' reply had begun poorly with Scott Brant removing the openers Richard Montgomerie and Murray Goodwin as they slumped to 53 for 3, but Cottey and Ambrose batted with great application to revive their side.
Cottey followed up his 188 in the innings victory over Warwickshire with another battling knock which occupied four-and-a-quarter hours. He moved to 99 by sweeping the spinner James Middlebrook for six, and his 211-ball vigil had also included 10 boundaries when he hooked a delivery from Dakin to Middlebrook at deep square leg.
Ambrose had departed in the previous over off the bowling of Grayson, having faced 170 balls and hit 12 fours. The former Zimbabwe captain Andy Flower dived full length to his right to take a fine catch at slip after Ambrose got a leading edge.
Graham Napier had earlier finished unbeaten on a Championship-best 89 as Essex, resuming on 305 for 8, added 35 before being dismissed.Reuse content