Rymell showed maturity beyond his four List A appearances to craft 78 as he put on 115 with Feroze Khushi – who clocked up 77 on the back of a century at Durham last time out.
Adam Wheater smashed a quick-fire 53 as the Eagles wracked up 321 for eight, which the Sharks never looked like chasing – getting bowled out for 224 with Travis Head top-scoring with 38 in front of a sold-out Cloudfm County Ground, Chelmsford.
Sussex Sharks captain Tom Haines said: “We are disappointed to lose but overall we lost to the better side today. They came into the game favourites but we came in confident after out last result.
“With the short boundary we thought that if we could get to 40 overs two or three down then we could chase a hundred plus but that didn’t go to plan. The boys in the middle order got started and would have liked to go on but the scoreboard pressure probably didn’t help.”
Essex face Lancashire in their last group game on Thursday; if they lose they’ll play an away quarter-final, if they win and Durham also win they’ll have a home quarter-final, while a victory at Emirates Old Trafford and a Durham defeat to Hampshire will see Eagles progress straight to a home semi-final.
Essex, having been put in, lost Alastair Cook and Tom Westley within the first eight overs – bowled and smashed straight at point respectively – before Khushi and Rymell patiently built the foundations of a large total.
The 20-and 22-year-olds showed patience and ran hard rather than peppered the boundary for much of their stays – although both the 50 and 100 stands were brought up with sixes off Rymell’s bat, coming in 76 and 127 deliveries respectively.
Rymell, who had been promoted to open, reached his maiden half-century in 70 balls but departed for 78 when he was lbw to 78 – ending a 115-run stand.
Khushi reached the milestone in one few ball and along with the hard-hitting Paul Walter put on 54 in 39 balls before an Essex wobble.
Walter top-edged to fine leg before Ryan ten Doeschate and Khushi were caught in the ring within nine balls of each other.
But the Sharks’ fightback didn’t last as Wheater launched an assault of three sixes and three fours to score 53 in 29 balls – his fifty coming after two successive maximums although perished attempting a third, with Simon Harmer lbw soon after.
Aron Nijjar teed off with a 16-ball 28 to get the Eagles over 300 and set their highest total of the campaign.
The chase began with Ali Orr surviving a regulation drop by Westley on three but chopped Jack Plom on having only added a further seven runs, before skipper Tom Haines edged Plom to slip.
Ben Brown slapped spinner Nijjar’s third ball to midwicket and Travis Head was bowled by Harmer – both getting starts but neither managed to settle like Khushi or Rymell.
David Wiese exploded with 36 off 20 balls, during a 52-run stand with James Cole, before splicing to midwicket and Oli Carter thrashed out to deep midwicket.
Sharks’ inexperienced lower-order couldn’t match Wheater, Walter and Nijjar’s hitting as Coles and Danial Ibrahim were both caught behind.
Will Beer was extraordinarily caught by Harmer at mid-on and Archie Lenham was snatched at mid-off – as ten Doeschate returned figures of four for 34.