Derbyshire 137 for 3 (Madsen 47) beat Gloucestershire 135 for 7 (Cockbain 45*) by seven wickets

Derbyshire may go into their first Finals Day in a fortnight as rank underdogs, but Essex, Nottinghamshire and Worcestershire will underestimate them at their peril. Victory here in the last of the Vitality T20 Blast quarter-finals was deserved, emphatic, and based on the same hard-nosed template of cricketing nous that has served Gloucestershire themselves over the years.

Having restricted the home side to a total some way below par, their prolific top-four batsmen all but knocked off the target of 136 on their own, victory arriving with 17 balls to spare. Billy Godleman, Luis Reece, Wayne Madsen and Leus du Plooy had struck 1,384 runs between them in the North Group stage; they will head to Edgbaston on September 21 with that total now on exactly 1,500.

"It is a huge relief, not just to me but to everyone involved with the club," Madsen admitted after receiving the Man of the Match award for his 47. "It has been a great day for us. We have developed a good culture in T20 and in the last seven or eight games we have really clicked. The supporters deserve this and we will go to Edgbaston with a lot of confidence."

As the 18th and last county to make Finals Day since the competition was inaugurated in 2003, Derbyshire have taken their time to get here. But the club blueprint with a specialist coach for the format in Dominic Cork is sure to be examined by the rest given unprecedented interest in the Blast this season. Spare seats, again, were rare dots in the crowd, and spectators were cramped just as tightly on the balconies of the flats behind the Ashley Down Road end.

Godleman wisely chose to field first given the peculiar appearance of the pitch. It was so green the stumps might have been hammered into the wrong part of the square, but he and his bowlers quickly assessed its true, slowish and slightly two-paced character. With the fielding display matching the discipline with the ball, Gloucestershire fell well short of the average first-innings score here this season, of 164.

Batsmen received few opportunities to challenge the shorter, straight boundaries, and the wagon wheel deceives because two of the sixes that look the result of fierce return drives were actually top-edged pulls. After a reasonable start, Gloucestershire found themselves strangled by the medium pace of Alex Hughes and Matt Critchley's wrist spin. They never recaptured any momentum given by their opening pair.

Michael Klinger ran into such good form at the end of the South Group stage - 264 runs in four innings - that he claimed to be re-thinking a decision to retire, but his dismissal in the ninth over proved a critical moment and has almost certainly persuaded him that he was right first time. Miles Hammond had already pushed to cover following an enterprising start and James Bracey reverse flipped to short third man, leaving a rebuilding operation once Klinger failed to beat Ravi Rampaul's throw from the edge of the circle.

In fact, Derbyshire conceded only 38 runs in the eight overs immediately on from the Powerplay. Crucially, they continued to make inroads, and the catch by Critchley off his own bowling to remove Jack Taylor was so well-judged and athletic, running back to his right and finally diving to hold the ball one-handed, that he deserved his name twice on the dismissal: ct Critchley b Critchley.

Much now hinged on Ian Cockbain, and for all his swings into the leg side, Derbyshire made sure that boundaries never came in clusters. Rampaul was exceptional at the end, changing pace and finding yorker-length, and went above Matt Parkinson at the top of the wicket-taking list for the season when Andrew Tye became his 22nd victim, fittingly to a full-length ball.

"I think we needed a minimum of 160," Klinger admitted. "The pitch played pretty well, the odd one held up but we knew Derbyshire were going to take pace off the ball anyway." He could only lament the absence of Benny Howell to a serious hamstring injury, though the serious damage had been done by the time their leading exponent of dibbly-dob would have joined the attack.

Madsen said as much, modestly deflecting his own sensible effort in praising the explosive start supplied by Godleman and Reece. Having identified the Powerplay overs as the most propitious time to attack, they were so positive that the required rate fell to below a run per ball by the end of the third over, Godleman bringing out the Australian fire in Tye by charging the pace bowler during a short, captivating passage.

They fell in successive overs and Madsen was a shade fortunate that his first boundary, with Tye bustling in as Mike Procter used to at the ground, sailed only inches high of cover. From then on, he found leg-side gaps expertly and with the boundaries fully patrolled the singles and hard-run twos made for very easy pickings. That was all Derbyshire needed.

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