The White Rose had won their two previous quarter-finals at the ground - in 2015 and 2018.
But hopes of a hat-trick were dashed as they failed to book a return to Cardiff for Monday’s semi-final – four days after a narrow win over Glamorgan in their final group game secured a place in the knockout stages.
In the end, it was a simple 129-run triumph for Essex, who totalled 317-7 from their 50 overs after choosing to bat.
Yorkshire did well to restrict them to 123-3 at the 30-over mark, but the hosts hammered 194 from the final 20 overs, including 118 off the last 10, to make what had threatened to be a manageable chase a mountainous one.
Josh Rymell, a 20-year-old opener, top-scored with 121, his maiden hundred, with four other players chipping in with 30s. George Hill was the pick of the Yorkshire bowlers with 3-51, Ben Coad taking two wickets and the two Matthews, Revis and Waite, one apiece.
Yorkshire never looked like chasing the runs, collapsing from 68-1 to 125-7 with all six wickets falling to spin – two each for Simon Harmer, Aron Nijjar and Tom Westley.
Westley, the Essex captain, added another to finish with his side’s best figures of 3-33, just shading the return of pace bowler Jack Plom (3-34).
Matthew Revis top-scored with 42, including a couple of leg-side sixes, and Will Luxton played well for 34. Will Fraine and Waite both hit 31, the latter enjoying himself at the death with three sixes in a 27-ball innings.
But it was a disappointing finish to a campaign that had sparkled at various points and which gave useful experience to a number of youngsters, meaning that Yorkshire’s wait for a one-day trophy will now extend into a 20th year.
Gary Ballance, the Yorkshire captain, said: “It’s disappointing to lose. I actually think we bowled well for the whole innings. They just got away from us in the last 10-12 overs. A few of their lads played well and gave them the momentum.
“With the batting, we lost too many wickets in the middle overs. When you’re chasing a big score, it’s quite hard to recover from that. But, credit to the lads, we’ve played some very good cricket over the last few weeks. There’s a lot of guys who’ve made a lot of improvements, have learnt a lot and will be better for the experience.”
In sunny conditions, Rymell paced his innings superbly, although he had a life on 36 when dropped by Dom Bess at cover off Hill. Paul Walter contributed a run-a-ball 33, Adam Wheater a momentum-changing cameo of 34 from 20 deliveries, and Harmer (31) and Nijjar (23) added an unbroken 50 from just 22 balls.
Fraine and Luxton shared 63 after Duke was bowled in the third over of the reply.
But when Fraine holed out into the leg-side off Harmer and Luxton was lbw to Nijjar, the left-arm spinner, Yorkshire’s challenge fell away. Hill picked out mid-on, Jonny Tattersall was bowled trying to cut, Ballance was trapped lbw on the back foot and Bess caught slicing to backward-point.
Revis’s gutsy innings ended when he was bowled endeavouring to pull, before Waite was stumped going for a big one and Coad caught at mid-on, Yorkshire all out with 12.2 overs of their innings unused.