Northants Steelbacks, Sussex and Leicestershire secured the last three places for the T20 Blast quarter-finals after the final round of group games.
The Steelbacks beat Birmingham Bears despite 119 off 64 balls by Adam Hose, and Sussex saw off 2019 winners Essex.
Leicestershire edged out the Bears on net run rate after defeating Lancashire Lightning at Emirates Old Trafford.
Elsewhere, Shaheen Afridi took 6-19, including four wickets in four balls to seal Hampshire's win over Middlesex.
There were also victories for Notts Outlaws, Gloucestershire, Glamorgan, Yorkshire and Surrey.
Gloucestershire, Notts, Lancashire, Surrey and Kent had already ensured they would be in the last eight before Sunday's matches, which ended a truncated county season for eight other teams - Derbyshire, Durham, Glamorgan, Hampshire, Middlesex, Warwickshire/Bears, Worcestershire and Yorkshire.
The quarter-finals will all be played on 1 October, with Notts at home to Leicestershire, Surrey playing Kent, Gloucestershire taking on Northants and Sussex facing Lancashire.
Finals Day will follow two days later, a date chosen in the hope the government will allow some spectators to be present at Edgbaston.
Bears home and Hosed - not quite
The Central Group game of the day saw Birmingham Bears reduced to 20-4 after 3.3 overs before Hose and Dan Mousley shared a stand of 171 to see them to 191-5.
Hose was run out off the final ball of the innings as Mousley finished on 58 not out, but their total was not enough, with Tom Taylor (50 not out off 27 balls) and Graeme White (37 not out off 12) putting on 53 to see Northants home by three wickets on 193-7 with seven balls to go.
Lewis Gregory's 50 led Bob Willis Trophy finalists Somerset to 161-7 at Bristol but their chance of going further in the competition were dashed as Ian Cockbain's 89 and a final-ball-of-the-match boundary by Tom Smith saw group winners Gloucestershire to 163-8, and a two-wicket win.
Cockbain hit three sixes and nine fours and surpassed Michael Klinger as the club's leading T20 run-scorer in the course of his innings.
At New Road, Hamish Rutherford made exactly 100 off 62 balls in a score of 190-3 by Worcestershire Rapids, but Glamorgan reached 196-4 with two balls spare to win by six wickets.
Foxes leave it late
Leicestershire and Durham both had a chance of going through from North Group at the start of play, but the latter went down by 18 runs at Trent Bridge as they were bowled out for 132 in response to 150-6 by Notts Outlaws.
Yorkshire Vikings beat Derbyshire Falcons by six wickets in a dramatic finish at Emerald Headingley as Harry Brook hit the final ball of the game for four.
He made an unbeaten 50 and put on 91 with England's Joe Root, whose 60 not out was his fourth half-century in five T20 appearances this season, as they reached 171-4, replying to Derbyshire's 167-6.
The final game of the day to finish was in Manchester, where Leicestershire Foxes posted 154-5 after being given an aggressive start by Nick Welch (43), who hit two sixes in Saqib Mahmood's opening over.
Arron Lilley top-scored with 49 but Lancashire were well-placed at 112-1 before four wickets went down for two runs in the space of seven deliveries, three of them in one over from Colin Ackermann.
Among his victims was opener Alex Davies, for 52, and the home side came up short on 132-5 as the Foxes - the only three-time T20 champions - squeezed into the quarter-finals.
Their net run rate of -0.18 was better than -0.63 by Birmingham Bears in Central Group.
"I'm unbelievably proud," head coach Paul Nixon told BBC Radio Leicester. "For us it's about standing up and really believing and knowing we can win against big teams."
Roy in racing mode
Kent's Daniel Bell-Drummond passed 400 T20 runs this summer in his 37 against Surrey in South Group, but it was England's Sam Billings who drove them to a score of 159-8 with his 50 off 33 balls.
Group winners Surrey made it seven victories out of 10, though, as Jason Roy (72 off 52 balls) and Laurie Evans (73 off 45) added 135 in 14 overs as they reached 161-4 in the 19th over.
Sussex climbed above Kent into second place, and secured a home quarter-final as they beat Essex, who were 0-2 after the first four balls of the game, by four wickets.
Paul Walter's 76 off 45 balls helped Essex to 136-9, but only two other batsmen reached double figures and the Sharks breezed to 137-6, thanks mainly to Phil Salt's quickfire 42 and 40 from Scotland's Calum MacLeod.
Hampshire ended a disappointing campaign on a positive note as their score of 141-9 proved enough for a 20-run win over Middlesex, only their second success in 10 matches.
Stevie Eskinazi's 16 was enough to take him past 400 T20 runs, but Pakistan's Shaheen Afridi produced figures of 6-19 - including taking the last four wickets in successive balls - as Middlesex were all out for 121.
Only three bowlers - Ackermann (7-18), Arul Suppiah (6-5) and Tim Southee (6-16) have better figures in an English T20 game, and Tim Bresnan also took 6-19 for Yorkshire against Lancashire in 2017.