The hosts needed 47 runs from the final four overs, but got home with a ball to spare to chase a revised target of 161 off 18 overs and win by three wickets.
Stephen Parry hit an unbeaten 22 from nine balls and pulled the winning boundary off Shiv Thakor.
Derbyshire earlier made 132-2 from 21.3 overs when rain halted their innings.
The home side took 39 from the first four overs, but were halted by the leg-spin pair of Jeevan Mendis (2-38) and Matt Critchley (1-23), along with the impressive medium pace of Thakor (3-23).
As wickets fell at regular intervals, Lancashire looked to be out of the game with four overs to go, but Steven Croft (26 not out) and Ryan McLaren (16) took 15 from Mendis' final over.
When McLaren and Haseeb Hameed fell in the next over, Lancashire required 24 from two.
It was then that Derbyshire fell apart. Croft was dropped at third man by Mendis off the bowling of Hardus Viljoen, a Ben Cotton mis-field at square leg gave Parry a boundary, with two fielders colliding at third man to hand Parry four more. In all, 17 came from the over.
And though Thakor had nailed his yorkers all evening, he could not prevent Parry from completing the job at a partisan Stanley Park.
Thakor earlier made 38 on a frustrating, wet afternoon that was illuminated by the cover drives of Derbyshire opener Ben Slater.
Slater hammered 60 as Derbyshire looked well placed for a big total in an innings already reduced to 36 overs, with the rain arguably giving Lancashire a more manageable chase on the DLS method.
Their victory means they will definitely make the quarter-finals if they win their last two games, while Derbyshire are all but out.
Lancashire pulled off a stunning run-chase to defeat Derbyshire and keep their hopes of reaching the One-Day Cup quarter-finals alive.