Dan Lawrence struck an unbeaten half-century and Mohammad Amir took four wickets as Essex kept their chances of qualifying for the Vitality Blast knockout stages alive at Hove.
Lawrence smashed 59 off 43 balls to lift the visitors to 168 for five after the home side won the toss.
Despite a 37-ball 66 from David Wiese, Essex claimed a nine-run win as Amir took four for 29, condemning Sussex to only their second defeat of the South Group campaign.
Chris Morris and Kyle Abbott each claimed three wickets as Hampshire kept their Vitality Blast hopes alive with a seven-wicket win over Middlesex at Lord's.
The South African pace duo helped bundle out the hosts for 128 before James Vince's 69 made short work of the chase.
Hampshire moved to 10 points, three behind their opponents in South Group with three games to play.
