The Nottinghamshire captain, Paul Johnson, hit three sixes and six fours in an unbeaten 85 off 61 deliveries to guide his side to their seventh win in eight games.
Set 195 in 33 overs after three interruptions they made light work of it, ending with 16 balls to spare.
Somerset's fifth Sunday win in succession keeps alive their hopes of finishing in the prize money. Marcus Trescothick's unbeaten 61 off 48 deliveries helped Somerset to 221 for 5 and Dean Jones' 81 off 104 balls looked to have Derbyshire cruising with 10 overs left but wickets tumbled and they finished 12 runs short.
Steve James and David Hemp put together a match-winning stand of 136 for the second wicket to enable Glamorgan to defeat Hampshire at Southampton. James hit 91 and Hemp was 64 not out when Glamorgan clinched victory by seven wickets with seven balls to spare.Reuse content