Faced with a daunting run-chase after James Foster's 65 not out led the Eagles to 177 for four, Sussex got home in a thrilling finish with just one delivery to spare.
When Ryan ten Doeschate began the final over, they still required 10 for victory, but Will Beer rose to the occasion by scoring nine from the first four balls, after which Ben Brown found a boundary to seal the win.
The foundations for their success had been laid by openers Chris Nash and Luke Wright, who raised the 50 in the sixth over and took the total to 77 before the former, on 31, hit Reece Topley to James Franklin at long-on.
Wright, with the help of three sixes and four fours, went on to make 46 from just 26 deliveries before Greg Smith held on at the boundary following another big hit. Matt Prior kept the momentum going with a 19-ball 35 that included two sixes among his five boundaries.
Sussex required just 36 from the final five overs and, despite losing a couple of cheap wickets, managed to hold their nerve to get home. Essex were indebted to an outstanding captain's innings from Foster, who struck five fours and four sixes during his 31-ball stay.
The wicketkeeper-batsman's dominance was best underlined by the fact big-hitting Adam Wheater contributed only five to their 65-run stand.
Foster's fireworks arrived after Graham Napier and ten Doeschate had threatened to tear the Sussex attack apart; both hit three fours and two sixes before falling without delivering substantial innings.
Napier was first to go, caught by wicketkeeper Brown, who atoned for dropping a chance off the same batsman two overs earlier, for 32. Ten Doeschate was caught low down on the midwicket boundary for 39 and the Eagles were left rueing his and Napier's failure to capitalise on fine starts.