The opener Robinson stroked 15 fours off 168 balls as Essex, set 282 to win, eased home with seven balls to spare on Saturday to register their highest winning score when batting second in the competition.
Essex lost their Australian Stuart Law for a duck to Jason Lewry, but Robinson added 153 in 25 overs, with the captain Nasser Hussain contributing 62.
Sussex have now lost both their opening matches and look set for an early exit for the 11th time in 12 seasons despite 87 from Australian Michael Bevan, who shared a second-wicket stand of 160 with Keith Greenfield. The youngster made a competition-best 93 not out.
Scotland's Jim Love was the more satisfied coach despite his side's three- wicket defeat by his former county Yorkshire at Linlithgow. Yorkshire, set a target of 169, surrendered wickets regularly with James Brinkley and Asim Butt claiming four quick wickets between them.
Yorkshire had to be thankful for the partnership of 49 between Richard Blakey and Darren Gough to scrape their second win of the competition.
Leicestershire bounced back after their defeat by Lancashire yesterday with a comfortable eight-wicket victory over Nottinghamshire at Trent Bridge.
Chris Lewis, who had a turbulent four-year spell with Nottinghamshire, played a key role in the downfall of his former team-mates. The England all-rounder had a hand in three dismissals midway through the innings which sparked a collapse.
Nottinghamshire had made steady progress in the early stages with Paul Pollard and Usman Afzaal compiling a stand of 104. Pollard departed shortly after reaching his 50 and as Nottinghamshire tried to accelerate in the final 20 overs, they lost wickets at a rapid rate. Afzaal reached a competition- best 78 but only two other Nottinghamshire batsmen reached double figures.
The Nottingham shire total of 196 for 8 was soon made to look inadequate once Leicestershire's Iain Sutcliffe and Phil Simmons came together. They shared an unbroken third-wicket stand of 143 in which Sutcliffe reached his first century in the competition and finished on an unbeaten 105. Simmons played the supporting role with 48 as Leicestershire cruised home with more than four overs to spare.
Kent celebrated their first cup win, after a rain-affected draw in their opening match, with a three-wicket last-ball victory over Gloucestershire at Canterbury. Matthew Walker was top scorer for Kent with 57, while Mark Ealham added 32 to help Kent pass Gloucestershire's score of 195 for 9. Courtney Walsh took three wickets for Gloucester but Ealham's three wickets for Kent proved more decisive.Reuse content