Matt Critchley took 3-133, but the Sussex top order scored quickly to set Derbyshire 405 runs to win in their final innings at The 1st Central County Ground.
Derbyshire were bowled out for 389 on the morning of Day Three, as Billy Godleman top-scored with 122 and there were half-centuries for Wayne Madsen (72) and Alex Hughes (77).
Phil Salt hit a first-class best of 148 as Sussex set Derbyshire a record chase, before openers Godleman and Ben Slater remained unbeaten overnight with the score 6-0.
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