Fraine smashed 50 off only 19 balls and his unbeaten 69, which contained five fours and four sixes, from 32 deliveries took Yorkshire to their target of 109 with eight balls to spare.
Derbyshire had set a challenging total of 108 for 6 after rain delayed the start by six hours with Fynn Hudson-Prentice hammering four sixes in an unbeaten 38 from 17 balls.
Josh Sullivan took four for 11, including three in four balls, with his leg spin before Fraine’s assault carried Yorkshire home at a canter and keeps alive their chances of making the knock-out stages.
Mitch Wagstaff and Harry Came got Derbyshire off to a good start when the rain finally cleared, adding 40 before Wagstaff was bowled trying to ramp George Hill in the fifth over.
Only finishing missing in another fine Mansfield Town display says boss Nigel Clough, but injury list lengthens for his depleted squad in Leyton Orient defeat
One more new face in for Mansfield Town as early injuries mount?
Mansfield Town made to pay for missed chances as they lose at Leyton Orient
See who you can pick out in our fans gallery from Mansfield Town v Derby County
Former Mansfield Town boss Mick Jones dies aged 75
Tom Wood drove Hill for consecutive fours but then became Sullivan’s first victim when he pulled the leg-spinner’s first ball to deep midwicket.
Brooke Guest was stumped coming down the pitch and Alex Hughes clipped his first ball to square leg as Derbyshire slipped to 50 for 4.
Hudson-Prentice pulled Mathews Pillans for six and Came repeated the treatment as 21 came off the seventh over.
Sullivan was driven over the long on fence by Hudson-Prentice but Came’s attempt to dispatch the spinner into the crowd ended in a sliced catch to cover.
Derbyshire needed another big over and Hudson-Prentice delivered when he straight-drove and pulled Ben Coad for sixes with 17 coming from the 9th.
It lifted Derbyshire to a competitive total but Fraine got Yorkshire off to a flyer, driving Hudson-Prentice for successive fours before lifting him over long off for six.
Matthew Revis miscued a pull at Ravi Rampaul to mid on but Fraine drove Mattie McKiernan for another six to take his side to 43 for 1 after three overs.
McKiernan bore the brunt of Fraine’s onslaught, conceding 21 from his second over, as the opener drove him onto the pavilion roof before his fourth six took him to a 19 ball 50.
William Luxton pulled George Scrimshaw for six and although he holed out to deep midwicket in the same over, Yorkshire needed only eight off the last two overs.
Gary Ballance removed any lingering hopes Derbyshire might have entertained of pulling off a dramatic heist by driving Hudson-Prentice for six as Yorkshire cruised to victory in the evening sunshine.