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Durham and Gloucestershire claimed the last two T20 Blast quarter-final places as Moeen Ali hit 103 off 59 balls for Birmingham Bears to end Leicestershire's hopes of progress in the competition.
Durham beat Derbyshire by eight wickets, thanks to an unbroken stand of 88 between Alex Lees and Colin Ackermann, while Essex's loss to Hampshire meant Gloucestershire - who were not playing - went through on net run-rate.
Also in South Group, Glamorgan's Kiran Carlson smashed eight sixes in making 135 off 64 balls, the highest T20 score for the county, as they totalled 243-4 against Somerset. Marnus Labuschagne then took 5-11 as the holders were bowled out for 123.
Elsewhere, there were wins for Sussex Sharks, Kent, Northants Steelbacks and Notts Outlaws.
Quarter-final draw
Surrey v Durham - Tuesday, 3 September
Sussex Sharks v Lancashire Lightning - Wednesday, 4 September
Northamptonshire Steelbacks v Somerset - Thursday, 5 September
Birmingham Bears v Gloucestershire - Friday, 6 September
The four winners will go through to Finals Day at Edgbaston on Saturday, 14 September.
Foxes fall short at final hurdle
When play began, Leicestershire were fourth in North Group, a point ahead of Derbyshire, Yorkshire and Durham, but their hopes of reaching the knockout phase were undone by Moeen's dazzling knock.
He set the tone by hitting Josh Hull's first two deliveries for four as he raced to 50 off 27 balls in an opening stand of 99 with skipper Alex Davies (31).
The left-hander struck nine sixes and seven fours before being caught off Hull at the start of the final over as Birmingham Bears posted a score of 194-5.
Leicestershire's chase never got going after their first three wickets fell in the space of nine deliveries and Lewis Goldsworthy's 35 was the only score of note as they were all out for 122 in 16.4 overs to lose by 72 runs - Danny Briggs taking 3-30.
Derbyshire Falcons scored quickly at the start of their innings against Durham but also lost wickets regularly and only managed a score of 155-8.
Durham, who began the match seventh in the table, approached their chase in controlled fashion and were 71-1 in the ninth over when spinner Alex Thomson sent back David Bedingham, caught by Samit Patel, for 15.
The visitors needed 81 from the final 10 overs and Lees and Ackermann did not need the final seven deliveries as an unbroken stand of 88 sealed an eight-wicket win on 159-2 - Lees finishing 72 not out from 60 balls and his partner on 54 off 30.
Yorkshire had home advantage against Notts Outlaws, but T20 debutants Freddie McCann (48) and Sammy King (44) put on 87 for the second wicket and Jack Haynes made 50 off 21 balls as the visitors posted 209-9 despite Ben Cliff's 4-31 - their best score in the 2024 competition.
The Vikings lost Adam Lyth and Shan Masood to successive Luke Fletcher deliveries in their reply and although James Wharton (56) and Jordan Thompson (50 not out off 29 balls) fought back they were well short on 181-6 as Notts managed only their third win, by 28 runs.
South African opener Matthew Breetzke scored the fastest 50 of the night - from just 19 balls - as Northamptonshire Steelbacks defeated Lancashire Lightning by four wickets with eight balls to spare at Old Trafford.
Paceman Jack White (3-16) dismissed Luke Wells and England's Phil Salt in the same over as Lancashire totalled 201-9 in their 20 overs, but Breetzke and Ricardo Vasconcelos (36) led the chase by sharing 102 in just 7.5 overs.
Both fell to spinner Wells - Breetzke for 76 from 31 balls - but Ravi Bopara (36) and David Willey (26) saw them to 189-3 before the loss of three quick wickets, but it made no difference to the outcome as the Steelbacks eased to 203-6.
Glamorgan achieve best T20 total
Somerset suffered an evening to forget at Sophia Gardens as Glamorgan dominated the game from the outset. Captain Carlson and Will Smale shared an opening partnership of 169 in 14 overs - the highest in the Blast this season.
Carlson reached 50 from 28 balls and hit two successive sixes off Jack Leach as he took only 20 more deliveries to reach his century.
They were eventually parted when Smale was caught off Ben Green for 59 but Carlson went past Ian Thomas' T20 county record score of 116 not out against the same opponents in 2004 as they posted their highest total in the competition.
Somerset needed an equally inspired response from one of their batters, but wickets fell regularly after Tom Banton hit three sixes in an over off Dan Douthwaite and the writing was on the wall at 90-5 before they lost their remaining wickets, all taken by spinner Labuschagne, for 21 runs in the space of 3.3 overs.
Australian Daniel Hughes became the competition's leading scorer, taking his total to 560 runs, as Sussex Sharks cruised to a nine-wicket win over Middlesex at Hove.
Jack Davies made 52 off 35 balls, but Middlesex could only manage 159-9 as Ollie Robinson took 3-27 and Hughes's 96 off 54 balls - with three sixes and 12 fours - saw them to 161-1 with 22 balls to spare.
The game at the Utilita Bowl went down to the final over as Essex made a gallant attempt to chase a target of 182 against Hampshire following a dismal start - a victory which would have seen them qualify.
Ben McDermott made 64 off 48 balls and James Vince and Tom Prest 41 each in the home side's 181-5 and Chris Wood then removed Adam Rossington and Dean Elgar in the opening over of the reply.
The dangerous Michael Pepper (20) and Paul Walter also went in the same over leaving Essex on 41-4, but Charlie Allison and Luc Benkenstein kept them in the hunt with a stand of 86.
Benkenstein went for 54, made from 35 balls, as John Turner took 4-23 and the Eagles needed 15 off the final over, but could only score seven as they ended on 174-7 to lose by seven runs - with Allison left on 69 not out.
Group winners Surrey suffered defeat in their final game as Kent beat them by 86 runs at Canterbury - only their fourth win in 14 games.
An opening stand of 108 between Tawanda Muyeye (61 off 31 balls) and Daniel Bell-Drummond (58) gave the Spitfires the platform for a score of 217-5 and they then bowled Surrey out in 16 overs for just 131, with Jas Singh and Matt Parkinson claiming three wickets each.