Matt Critchley hit a fluent 86, but Leicestershire ran out six-wicket winners in the Specsavers County Championship match at The 3aaa County Ground.
The all-rounder batted resolutely with the tail and accelerated the Derbyshire innings, but wickets at regular intervals meant the hosts could only set Leicestershire 133 runs to win.
Colin Ackermann (58) and Paul Horton (48) made light work of the chase, and despite two wickets each for Duanne Olivier and Hardus Viljoen, Leicestershire chased down the total in the final session on Day Three.
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