Pakistan all-rounder Shahid Afridi (101) enjoyed one of his best batting performances for many years as he struck ten fours and seven sixes to help his side post 249-8 from their 20 overs.
The scoreboard pressure took its toll on Derbyshire as Kyle Abbott (3-25) and Liam Dawson (3-28) claimed three wickets apiece to send Hampshire to Edgbaston.
Hampshire had reached six successive semi-finals from 2010-2015, and they have bounced back emphatically following a disappointing competition in 2016.
They face Royal London One-Day Cup champions Notts Outlaws in the second semi-final on Saturday, with Glamorgan taking on 2014 winners Birmingham Bears in the first semi-final.
The strength of Hampshire’s batting line-up has been key to their progress in this year’s competition, with several internationals contributing to their success.
England’s James Vince has been the most consistent performer, scoring 486 runs at an average of 37.38 including four half-centuries. His former international teammate Michael Carberry averages 35.17, whilst former Australia captain George Bailey has 297 runs in the competition.
With the ball, wickets have been spread out and it has been two England spinners who have led the way. Mason Crane (17 wickets) and Liam Dawson (12 wickets) have both averaged under 18 with the ball, a phenomenal return in T20 cricket. Both men will have an important part to play at Edgbaston.
Notts Outlaws reached finals day by defeating Somerset by five wickets last week. England opener Alex Hales is set to be a key player with the bat, alongside the likes of all-rounders Dan Christian and Samit Patel.
Their bowling attack is also strong with England duo Jake Ball and Harry Gurney both very effective in the shorter format.
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