Defending champions Lancashire Lightning were knocked out of the NatWest T20 Blast on Friday despite their victory over the Birmingham Bears.
Durham Jets' 13-run victory over Derbyshire ensured the 2015 winners have failed to reach the quarter-finals, although their hopes were already slim at the start of play.
Durham will now face Gloucestershire in the last eight after Mark Stoneman inspired them to the win they needed to also knock out the Bears following their slip.
Elsewhere in the quarter-finals, Notts Outlaws will play the Essex Eagles, the Northamptonshire Steelbacks host Middlesex and Glamorgan welcome the Yorkshire Vikings.
Stoneman's unbeaten 82 helped fire Durham to victory as Calum MacLeod also hit 83 from 50 balls in their 193 for two - despite Neil Broom's 68, Derbyshire fell short.
Lancashire's 30-run win over Birmingham meant nothing. D espite only posting 124 for five, with Tom Moores hitting 39, they defended it as, after Ian Bell walked for 13 in the fourth over, the Bears never recovered.
Sam Hain grabbed 28 but the visitors could not cope with Arron Lilley (two for 21) and Saqib Mahmood (three for 10) and made 92 for eight in reply.
Glamorgan's game in Essex was rained off after the visitors had posted 184 for five following Colin Ingram's 101 but the point gave Essex what they needed to reach the last eight.
It knocked Surrey out in dramatic style after Jason Roy's unbeaten 120 from just 62 balls demolished Kent. The hosts' total of 212 for four was too good for Kent, who are also eliminated, as they lost by 37 runs.
Gloucestershire beat Middlesex by four wickets with three balls to spare to win the South Group. John Simpson plundered an unbeaten 40 as Middlesex posted 156 for five but Jack Taylor hit four sixes in his 44 to inspire Gloucestershire to a 10th win in 14 matches.
Yorkshire reached the quarter-finals against already-qualified Northamptonshire with a 14-run win at the County Ground.
The visitors, after winning the toss and electing to bat, hit 177 for five thanks to Alex Lees' 59 and Jack Leaning's 64.
Northants opener Josh Cobb was then dismissed with the first ball of the hosts' innings and, while skipper Alex Wakely fired his way to 64, they fell short to make 163 for seven.
North Group winners Nottinghamshire beat Leicestershire by eight wickets on the Duckworth-Lewis method following their rain-interrupted game at Trent Bridge.
Leicestershire posted 170 for four in a game reduced to 18 overs each as Mark Cosgrove scored 53. In reply the hosts scored 146 for two with Michael Lumb unbeaten on 64.
Hampshire cruised past Somerset to win by 83 runs after bowling the visitors out for just 98 - as Liam Dawson took five for 17 - to avoid finishing bottom of the South Group.
The visitors never looked like beating Hampshire's 181 for three with only Jim Allenby (40) and Ben Green (12) reaching double figures. Tom Alsop had earlier hit 81, including four sixes, from 57 balls to set the hosts on the way to victory.
Source: PA
