The Pakistani all-rounder smashed 101, which included seven sixes and 10 fours, off only 43 balls to power Hampshire to 249 for eight - their highest T20 score.
Skipper James Vince made 55 from 36 balls as Hampshire passed their previous best of 225 for two against Middlesex in 2006 and, faced with an improbable target of 250, the Falcons crumbled to 148 all out with Liam Dawson and Kyle Abbott each taking three wickets.
Hampshire are now 9/4 favourites with Sky Bet to lift the trophy, ahead of Nottinghamshire at 3/1, Surrey 5/1, Glamorgan 11/2 and Birmingham Bears who are 8/1 with Somerset and Leicestershire both 12s.
Hampshire promoted Afridi to opener against the county he played for in 2003 and he swept and drove four boundaries from Wayne Madsen’s first over before Calvin Dickinson took two fours from Hardus Viljeon.
Dickinson was brilliantly caught one-handed by Matt Henry running back at mid-on for 18 off Ben Cotton.
Afridi’s previous high score in the competition this season was 18 but he pulled Cotton for six before driving him over the top of the three-storey media centre.
He reached his fifty off only 20 balls with a top-edged six but after driving Imran Tahir for another huge six, he was dropped on 65 at long-on by Madsen.
It proved expensive as Afridi dispatched Matt Critchley and Tahir for two more sixes on his way to a 42-ball hundred before he top-edged another big pull and was caught at long-leg.
By then the damage had been done, and Vince and George Bailey continued the plunder with the Hampshire skipper reaching his fifty with consecutive sixes off Cotton before wickets tumbled in the closing overs.
Critchley took three in the 19th as the leg-spinner finished with three for 32 but Hampshire’s score was the biggest ever at Derby and the fourth highest in domestic T20 matches.
Billy Godleman pulled the first ball of the Falcons reply for four but then swung Dawson to wide midwicket and Critchley followed in the next over.
Luis Reece drove Chris Wood for six before he was caught behind trying to run the ball to third man and when Madsen turned Abbott to backward square, the Falcons were sliding away at 35 for four.
The wickets continued to tumble and with the result a foregone conclusion, it was just a question of whether the Falcons could prevent Hampshire beating the biggest victory margin of 172 in T20 cricket.
Alex Hughes and Daryn Smit at least avoided that ignominy, before Cotton and Tahir shared a breezy last-wicket stand of 46, but it was scant consolation on a night of total Hampshire dominance.
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