Seventeen-year-old Fisher joined Rich Pyrah and Jack Brooks as the only Yorkshire players to take five wickets in a 20-over match as the Falcons were bowled out for 128 inside 19 overs on the way to a seven-wicket defeat with 20 balls remaining.
Fisher struck twice through the middle of the innings as Derbyshire, invited to bat, slipped from 66-1 in the ninth to 81-6 in the 13th, a loss of five for 15 in 25 balls.
South African Hashim Amla top-scored with 29, but him falling caught at cover off Pyrah hurt the Falcons badly.
A crowd of 5,953 saw Fisher record 5-22 from 3.2 overs before watching third-wicket pair Andrew Gale and Jonny Bairstow impress in Yorkshire’s chase with 41 off 36 balls and 40 not out off 35.
Tim Bresnan, Liam Plunkett and Adil Rashid all struck once for the Vikings, while Pyrah added an excellent 2-13 from his four overs. His wickets were part of the mid-innings collapse.
Fisher became the youngest post-war county cricketer when he debuted in a one-day match aged 15 in 2013, and he made his first Championship appearance earlier this summer.
He is currently out of consideration for four-day cricket due to A-Level exams, but he passed this test under lights with flying colours.
He broke a dangerous second-wicket partnership of 39 between Amla and Chesney Hughes (27) with his second ball by getting the latter caught at point.
He then trapped Shiv Thakor lbw in his second over before returning to get two wickets in the 17th over as Derbyshire slipped to 115-8.
He had Alex Hughes caught and bowled and Tom Poynton (27) caught behind at either end of the over, and he wrapped up the innings at the start of his fourth over by getting Ben Cotton caught and bowled running towards cover.
Cotton bowled Andrew Hodd for a golden duck two balls into Yorkshire’s reply.
Alex Lees then sliced Mark Footitt to third man in the fifth over, leaving the score at 31-2, but Yorkshire’s win was rarely in doubt.
Gale and Bairstow put on 69 inside nine overs, taking three sixes off former Yorkshire spinner David Wainwright in the 13th over.
Fisher said: “It’s been great under the lights here with a bumper crowd.
“We didn’t get off to a great start - we didn’t get our line and length right. But then I got the call, and I tried to hit my lines and went from there.
“It’s been a really good start to the season for me. I haven’t expected to play Championship or T20 cricket. The England lads have come back, and I didn’t think I’d play this game with the calibre that’s in the squad but (coach) Jason Gillespie’s shown faith in me, and I’ve paid him back.”
Wes Durston, Derbyshire’s captain, said: “That’s where the game was lost, through the middle of our innings.
“We had a decent power play and were happy with where we were after six overs (then) those batters that were set disappeared and no one could get in and form any partnerships.
“When you lose five for 20, it’s always going to be hard to post a total to defend.”