After a rain delay, Shiv Thakor top-scored with 60 as Derbyshire reached 209-8 from their allotted 36 overs.
Set a revised 218 from 36 overs on the Duckworth-Lewis method, Tom Kohler-Cadmore (63) and Daryl Mitchell (67) helped the visitors to a strong start.
Ed Barnard and Ross Whiteley then got them home with 24 balls to spare to secure a sixth win from eight matches.
Derbyshire, who could not qualify for the knockout stages following Sunday's defeat by Leicestershire, were put into bat and reached 34-1 after 10.3 overs before rain struck.
After play resumed at 17:00 BST with the game reduced to 36 overs per side, Barnard (3-37) and captain Joe Leach (2-43) helped Worcestershire take regular wickets to restrict the home side to 5.8 runs per over.
Australia spinner Nathan Lyon took 1-31 on his Worcestershire debut, after arriving as cover for compatriot John Hastings, who is now part of Australia's Champions Trophy squad for the next month.
Openers Kohler-Cadmore and Mitchell then broke the back of the chase with an opening stand of 90, before contributions from Tom Fell (24) and Brett D'Oliveira (18) helped them on their way, despite Hardus Viljoen's taking 3-55 with the ball.
Derbyshire fast bowler Hardus Viljoen told BBC Radio Derby:
"We are a young team. We've shown in patches in this competition that we can play good cricket but we are also still learning.
"You need to strike up front early on but the guy who scored 63 came in and played a knock out of his socks.
"That is going to happen. You can't take any credit away from him. He played well."
Worcestershire director of cricket Steve Rhodes told BBC Hereford & Worcester:
"I'm delighted for the players and the staff who put in the work and time to try and get that home semi-final.
"It's going to be a nice pay-day for the club and I'm very proud of what the team have done in finishing top of the group,
"We're a small club and we like to play our young academy players. We don't venture off too much with the non-English players and it's a nice feeling to finish top."
Worcestershire secured top spot in the One-Day Cup North Group and a home semi-final with a win over Derbyshire.