Half-centuries from Riki Wessels (50), Samit Patel (55) and Dan Christian (54) helped Notts make 284-8 in 50 overs.
Tom Fell (63*) and Daryl Mitchell (61*) saw the visitors to 138-1 off 24 overs - way ahead of the D/L par score - when rain ended the match at 19:45 BST.
Nottinghamshire were eliminated from the competition by the defeat.
Worcestershire started the match in sixth place in the North Group, level on points with Notts in fifth, with the top four going through to the last eight.
However, Durham's abandoned game at Old Trafford against Lancashire saw Worcestershire climb above them into fourth with a superior net run-rate.
Nottinghamshire looked to have posted a highly competitive score, as skipper Chris Read's unbeaten 39 off 26 balls in the final stages added to the earlier contributions from Wessels, Patel and Christian.
But Fell, a day after his 116 not out led Worcestershire to victory over Lancashire, and captain Mitchell batted aggressively in the rain to take their side into a winning position when conditions became unplayable.
Worcestershire booked a place in the One-Day Cup quarter-finals with a 35-run Duckworth-Lewis win over Nottinghamshire at Trent Bridge.