Reigning champions Northamptonshire crashed out of the NatWest T20 Blast after their final group game against Durham was abandoned.
Heavy rain at Wantage Road denied the Steelbacks the chance of claiming a top-four place in the North Group, although Durham were in pole position when the game was stopped.
Durham made 208 for three - their fourth-highest T20 total - with Graham Clark the chief aggressor in making 71 off 37 balls.
But the rain prevented the Steelback batsmen from recovering the game and securing a quarter-final spot.
Derbyshire Falcons booked a quarter-final spot by crushing Worcestershire Rapids by 48 runs at Derby.
Wayne Madsen scored 55 from 42 balls - his fourth 50 of the season - to take the Falcons to 146 for eight and then took a wicket as the Rapids slumped to 39 for five.
Tahir (four for 17) and Hardus Viljoen (two for 20) shone with the ball as the Rapids were bowled out for 98 in 15.4 overs.
Birmingham Bears made it through in to the last eight in beating Lancashire by two wickets with three balls to spare at as Old Trafford.
Dom Sibley (53), Ed Pollock (49) and Adam Hose (49) all made vital contributions to chase down Lancashire's 163 for four.
For Lancashire, who have failed to qualify for the last eight since winning the Blast in 2015, they had to win and hope other results went their way to qualify. But Jos Buttler's 58 off 42 balls proved to be in vain.
Cameron Delport's century led Leicestershire Foxes to a two-run victory over Notts Outlaws, which saw them join their hosts in the quarter-finals.
Delport (109 not out) scored his runs from just 59 balls, hitting nine fours and six sixes as the Foxes scored 203 for five.
Notts, who had already secured top spot in the North Group, fell agonisingly short after Dan Christian's 73 from 32 balls almost overcame a poor start - the Outlaws finishing on 201 for eight.
Glamorgan topped the South Group and secured a home quarter-final tie with a seven-wicket win over Middlesex.
Michael Hogan and Marchant de Lange took three wickets apiece as Glamorgan reduced Middlesex to 99 for eight in 14 overs in a rain-affected contest.
Adam Voges made an unbeaten 58 for Middlesex, but Glamorgan won with an over to spare as Aneurin Donald (33), Chris Cooke (25 not out) and Jacques Rudolph (22 not out) ended the visitors' hopes of qualifying for the knockout phase.
Surrey finished second in the South Group after holding their nerve to beat Kent by 10 runs.
Jason Roy was the mainstay of Surrey's modest 154 for nine with 78 from 43 balls.
Kent pair Joe Denly and Daniel Bell-Drummond - fresh from their previous night's world-record T20 opening stand of 207 against Essex - initially took a slightly more measured approach.
The Spitfires were well placed at 78 for one, but Rikki Clarke (four for 16) changed the course of the contest for Kent to miss out on the last eight for the second season running.
Peter Trego and Johann Myburgh crafted half-centuries as Somerset reached 189 for three to beat Hampshire by 98 runs and reach the quarter-finals.
After Somerset bowled Hampshire out for 91 - Craig Overton and Roelof van der Merwe both taking three wickets apiece - with eight balls to spare, they were forced to wait until the conclusion of the Glamorgan match to have their place confirmed.
Sussex Sharks beat Essex Eagles by 55 runs, but still went out of the competition as their net run rate was inferior to Somerset's.
Chris Nash top scored with 73 from 55 balls in the Sharks' 172 for four, his sixth half-century in this season's competition.
Essex were never in the hunt and were all out for 117 in the 16th over, with Will Beer taking three for 36.
Quarter-final draw: Derbyshire Falcons v Hampshire (August 22), Glamorgan v Leicestershire Foxes (August 23), Notts Outlaws v Somerset (August 24), Surrey v Birmingham Bears (August 25).
Source: PA
