Derbyshire defeated Gloucestershire by 53 runs to join their opponents in qualifying from Group A of the Royal London One-Day Cup.
The Falcons made 271-7 at Derby thanks mainly to Billy Godleman making a career-best score in List A cricket of 96 that included sharing in a 116-run stand for the third wicket with his captain, Wayne Madsen (57).
Although the hosts did lose four wickets for 31 runs, Scott Elstone (37) and Tony Palladino - who made an unbeaten 28 from just 14 deliveries – lifted the run-rate in the closing stages, despite a brief break for rain.
Gloucestershire's run chase wasn't helped by skipper Michael Klinger being forced to retire hurt after being struck on the arm by a short ball from Mark Footitt, who then went on to dismiss Gareth Roderick and Ian Cockbain in a hostile opening spell.
Chris Dent made 70 from 58 balls before being bowled by a beauty from left-arm off-spinner David Wainwright (3-45) and despite a breezy 53 from Jack Taylor, the Gladiators – who will now travel to Kent in the next round - were bowled out for 218 in 39.5 overs.
Derbyshire – whose qualification is even more impressive considering they started the campaign on minus two points as a punishment for a poor pitch last season – will now make the short trip to Trent Bridge to take on Nottinghamshire in the quarter-finals.
They jumped up to take fourth place in the table thanks to Leicestershire suffering an eight-wicket defeat at the hands of Lancashire at Old Trafford.
Kabir Ali's 3-26 and two wickets apiece for Tom Bailey, Steven Croft and Tom Smith saw the Foxes fold for 184 all out in 43.1 overs, opener Josh Cobb top scoring with 58.
Smith then completed a fine all-round match by making 54 in Lancashire's run chase, the same score managed by fellow opener Luis Reece, as the Lightning reached their target with 20 overs to spare.
Meanwhile, Yorkshire set up a home tie against Durham in the knockout stages with a resounding six-wicket victory over Hampshire in Southampton.
The home team were bowled out for 172 in just 39 overs despite a battling knock of 91 not out from skipper Jimmy Adams. Jack Brooks (3-30) helped reduce Hampshire to 31-3 before Adil Rashid spun his way through the tail.
The leg-spinner finished with career-best one-day figures of 5-33, including taking the last four in the innings as Hampshire collapsed dramatically from 161-5.
Alex Lees led Yorkshire's run chase with 61, while Adam Lyth (21) and Kane Williamson (33) made useful contributions before Jonny Bairstow’s unbeaten 45 saw the White Rose county home with just the 127 balls remaining.
Essex rounded out their group campaign with a four-wicket victory over Northamptonshire, passing their opponents’ total of 311 in the final over at Wantage Road.
Stand-in skipper Mark Pettini made 88 and there were half-centuries from Tom Westley (62) and Ravi Bopara (61) in the away team's successful run chase, meaning David Willey's fine knock of 113 earlier in the day wasn't enough for the Steelbacks to finish their 50-over season with a flourish.
The Eagles will next take on Warwickshire – it is the second time they have met in the last eight of a competition this year, the Bears having beaten the Eagles at Chelmsford in the NatWest T20 Blast.