After Colin Munro (49) and Ben Cox (46) helped the Rapids post 162-9, Worcestershire captain Daryl Mitchell took 5-28, which included three caught and bowled dismissals, to secure his side a 31-run victory and put the holders on the verge of elimination.
Prolific opener Jason Roy missed out for Surrey at Cheltenham, but there were contributions from the whole batting lineup, with Tillakaratne Dilshan top scoring with 36, as the London outfit made 157-8.
Michael Klinger struck 45 opening for Gloucestershire, but Zafar Ansari claimed 3-37 to keep the home side behind the rate, and late hitting from Benny Howell (29) and Jack Taylor (19) was in vain as they came up five short.
Gloucestershire are unable to qualify for the next round, and neither are Sussex, who lost by six runs chasing down Hampshire's 177-3, which was inspired by Michael Carberry's unbeaten 87 and 52 from Jimmy Adams.
New Zealand international spinner Jeetan Patel took a hat-trick as Birmingham Bears maintained their hopes of progressing to the last eight with a five-wicket triumph over top-four rivals Yorkshire Vikings.
An unbeaten 69-run stand for the seventh wicket between Tim Bresnan (45*) and Adil Rashid (29*) helped the hosts post 147-6 at Headingley, and although Ryan Sidebottom helped reduce Birmingham to 40-4, Laurie Evans hit 69 from 44 balls to earn the Bears a crucial victory on the penultimate delivery.
Lancashire Lightning and Essex Eagles, leaders of the respective divisions, had already advanced to the knockout stages but their victories tonight mean that they will have home advantage in their quarter-final ties.
Derbyshire gave it a good go, with Marcus North (41) and Wayne Madsen (45) dishing out some punishment of their own, but two wickets from overseas paceman Junaid Khan on his final Lancashire appearance of the year secured them their ninth win of the season.
The Eagles are the only side in the country who can better that tally, and they made it 10 victories from 11 this campaign by knocking off Glamorgan's 157-2 with eight seven wickets and two overs to spare.
Glamorgan only used three batsmen in their innings as Jacques Rudolph carried his bat for 60 from 57 balls and Murray Goodwin was caught on the final ball of their 20 overs for a more aggressive 71.
Rob Key struck 72 and Sam Northeast 73 as Kent set their opponents a daunting 196 to win, and the former champions lost five wickets in seven overs to put them way behind the rate when the bad weather came.
Worcestershire Rapids (162-9) beat Northants Steelbacks (131 a/o) by 31 runs.
Surrey (157-8) beat Gloucestershire (152-7) by five runs.
Hampshire (177-3) beat Sussex Sharks (171-8) by six runs.
Birmingham Bears (148-5) beat Yorkshire Vikings (147-6) by five wickets.
Lancashire Lightning (225-7) beat Derbyshire Falcons (190-7) by 35 runs.
Essex Eagles (159-3) beat Glamorgan (157-2) by seven wickets.
Kent Spitfires (195-7) beat Somerset (59-5) by 40 runs on Duckworth-Lewis method.