Birmingham Bears, Hampshire Hawks and Sussex Sharks sealed quarter-final spots with victories on the final day of T20 Blast group-stage action.
The Bears and Hawks cruised to wins over Northamptonshire and Glamorgan, while the Sharks stunned in-form Kent.
Leicestershire's Josh Inglis made a sensational century to deny Worcestershire a last-eight place.
Somerset dashed Gloucestershire's hopes too as their win guaranteed a home quarter-final.
Surrey, who had already played their last group-stage game on Friday, also narrowly missed out.
Bears and Hawks get job done early
Both Birmingham and Hampshire had anxious waits after claiming early victories.
D'Arcy Short (69) top scored for the Hawks as they comfortably chased down Glamorgan's total of 184-4 despite Australian Marnus Labuschagne striking 78 from 47 balls for the visitors. Hampshire now face a trip to Notts Outlaws.
Birmingham debutant Chris Benjamin made an unbeaten 60 off 34 deliveries as they reached 191-6 against Northamptonshire, with the Steelbacks held to 177-8 in reply.
The Bears started the day behind Worcestershire in the North Group standings, but booked a date at Kent after the Rapids lost to Leicestershire.
Worcestershire set the Foxes a competitive 170 to win at Grace Road, but the hosts easily chased down the total with Inglis hitting a stunning 118 not out off 61 balls with 10 fours and eight sixes.
Hampshire, who won their final five matches to give themselves a chance of progress, sneaked into the top four of the South Group thanks to Gloucestershire's failure at Taunton.
Tom Lammonby was run out for 90 in the final over as Somerset posted 183-7. In response, Gloucestershire fell 23 runs short on 160-6, with the hosts securing a home last-eight tie against Lancashire, who had reached the knockouts with a win over Yorkshire on Saturday.
Sussex through and Notts make 221
Sussex knew victory would be enough to see them through - and duly produced a dominant performance against Kent.
The South Group leaders were limited to 130-7 at Canterbury, with Sussex and England paceman Jofra Archer bowling three overs in his first competitive match since May as he recovers from an elbow injury.
The Sharks cruised to 134-6 in their innings, winning by four wickets to set up a meeting at Yorkshire.
North Group winners Nottinghamshire went big in a 78-run success over Durham after Ben Duckett's 74 off 41 balls helped the hosts to 221-4 at Trent Bridge.
Outlaws bowler Calvin Harrison took 4-36 as their opponents were all out for 143.
The match also saw England and Durham bowler Brydon Carse require seven stitches after getting hit in the ear by a powerful low blow from Alex Hales.
There was also a rare victory for Middlesex, who edged Essex by nine runs with former England bowler Steven Finn taking 3-25.
Birmingham Bears (191-6 ) beat Northamptonshire Steelbacks (177-8) by 14 runs
Notts Outlaws (221-4) beat Durham (143) by 78 runs
Leicestershire Foxes (171-3) beat Worcestershire Rapids (169-6) by seven wickets
Essex Eagles (160-9) lost to Middlesex (169-5) by nine runs
Hampshire Hawks (187-4) beat Glamorgan (184-4) by six wickets
Kent Spitfires (130-7) lost to Sussex (134-6) by four wickets
Somerset (183-7) beat Gloucestershire (160-6) by 23 runs
The T20 Blast quarter-finals will take place from 24 to 27 August with Finals Day on 18 September.
Attention in domestic cricket now turns to The Hundred which begins on Wednesday 21 July when the Oval Invincibles host the Manchester Originals in the Women's Hundred live on BBC Two.
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