The two all-rounders combined impressively after a shaky start to the chase saw the hosts slump to 67-4 after ten overs.
Luke Wright was first to go as the Sharks' skipper was dismissed for a first ball duck. Then, Harrison Wards (22) was run out after a mix up with Ravi Bopara. Both Sussex batsmen ran to the same end as Ward’s exciting cameo was brought to a comical end.
Sussex continued to struggle as Travis Head (5) and David Weise (2) both fell cheaply.
However, Ravi Bopara's well-measured knock saw Sussex home as the former-Essex man was joined by Delray Rawlins for a brutal and unbeaten fourth-wicket partnership.
Despite Bopara bringing up his half-century with ease, with seven fours, it was Rawlins who starred with a compelling knock.
From the off, he found the fence on numerous occasions. The pick of his four sixes a towering strike over mid-on after the Bermudian international advanced down the wicket.
Later, Rawlins hit a six to not only win the match, but bring up his half-century in just 29 balls.
Earlier, Essex lost 4 wickets for 5 runs, with the hosts eventually dragging themselves to a first-innings total of 146-9.
England internationals Chris Jordan (3-30) and Ollie Robinson (2-15) excelled as Sussex’s seamers bowled through Essex’s middle order.
Sussex shone with the ball from the start. Robinson grabbed a wicket with his first delivery as Adam Wheater smashed straight to Ravi Bopara at extra cover. Robinson's second wicket was a beauty; a full straight delivery that smashed into Feroze Khushi's pads, leaving the Essex batsmen bemused.
Elsewhere, Chris Jordan, who was fresh back after a slight groin strain, picked up the vital wickets of Jimmy Neesham and Ryan ten Doeschate on his way to an impressive 3-for.
For Essex, Tom Westley (53) and Micheal Pepper (38) were the only two that troubled Sussex. The latter’s entertaining cameo was brought to an end by Archie Lenham, who once again proved to grab a vital wicket with Essex, at that point, 80-1 after ten overs.
The six-wicket win sees Sussex rise to second in the South Group, with one more win from their final two games likely to be enough for the Sharks to progress to the quarter-finals.