Derbyshire slipped to 47-4 but Alex Hughes led a recovery with 96 not out.
Gavin Griffiths took 3-44 and Dieter Klein 3-46 as the Foxes restricted Derbyshire to 219 all out.
Cameron Delport (53) gave the hosts a solid start, before Ned Eckersley (80) and Lewis Hill (68 not out) saw them home with more than 10 overs to spare.
Leicestershire move onto seven points from seven matches, while Derbyshire's hopes of qualifying for the knockout stages are over after two wins from seven games.
Derbyshire's total never looked enough and Hughes was the only man to make an impact with his 106-ball innings containing a six and 10 fours.
To underline their struggles, Matt Critchley was Derbyshire's second-highest scorer with 29 from 38 balls.
The Foxes successful run-chase never looked in any doubt despite losing Mark Pettini for one to South African Hardus Viljoen in the second over.
After Delport's half-century, Eckersley and Hill put on 116 in 17.4 overs to take Leicestershire to the brink of victory.
Eckersley was run out with two more required before Hill hit Jeevan Mendis to the boundary to win the game at a canter for the Foxes.
Leicestershire beat East Midlands rivals Derbyshire by five wickets to keep alive their hopes of a top-three finish in the One-Day Cup North Group.