Alex Hughes hit a career-best unbeaten 96, but half-centuries from Cameron Delport, Ned Eckersley and Lewis Hill guided Leicestershire Foxes to a five-wicket win at the Fischer County Ground.
Hughes was the mainstay of the Derbyshire innings, hitting 10 fours and one six, but he was left stranded four short of a maiden List A century, as three wickets for Gavin Griffiths (3-44) and Dieter Klein (3-46) dismissed the Falcons for 219.
Ben Cotton was the pick of the Derbyshire bowlers, claiming 2-18 off his nine overs, but fifties from Delport (53), Eckersley (80) and Hill (68 not out) saw the hosts to victory with 10 overs to spare.
The defeat means Derbyshire can no longer qualify for the knockout rounds of the Royal London One-Day Cup, with one fixture remaining, at home versus Worcestershire on Tuesday (2pm start).
After being asked to bat first, early wickets fell to put the Falcons on the back foot. Ben Slater was first out for 11, before Billy Godleman (9), Shiv Thakor (6*) and Wayne Madsen (7*) all fell in quick succession with Derbyshire 47-4 in the 11th over.
Jeevan Mendis and Hughes tried to rebuild and shared a 69-run partnership in 15 overs, before Mendis was fifth man out for 23.
Hughes led the scoring and passed fifty off 60 balls, but he continued to lose partners as Daryn Smit (12) and Luis Reece (5) were dismissed, with Derbyshire 137-6 after 31 overs.
New man Critchley was able to support Hughes, as together they added 55 runs in 12 overs and get their side over 200, before Critchley was out for 29.
Hughes finally ran out of partners and was left stranded on a career-best 96 not out off 106 balls, including 10 fours and one six, as Derbyshire were all out for 219 with 2.2 overs left in the innings.
Hardus Viljoen made the first breakthrough in the second over as Mark Pettini (1) was caught at slip by Hughes, but Cameron Delport and Ned Eckersley responded well sharing a 75-run stand in 13 overs.
Delport passed fifty, but was out shortly after, well caught behind by Smit off Thakor for 53 off 62 balls. Ben Cotton then removed new man Mark Cosgrove (1) in the following over to put the match back in the balance, with Leicestershire 77-3.
Cotton had his second shortly after, with Ali caught behind for 12, but Eckersley was in good touch and reached his half-century, with support from Lewis Hill.
Together they put on 116 for the fifth wicket to move their side to victory. Eckersley hit 80 off 81 balls, including eight fours, before he was run out two runs short of victory.
Hill hit the winning runs to end unbeaten on 68 off 66 balls, including 10 fours and one six, to see Leicestershire to victory. Derbyshire have one fixture left in the competition on Tuesday versus Worcestershire Rapids.
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