Sussex completed a nine-wicket win over Derbyshire before lunch on the final day.
Luke Wells (23no) and Michael Yardy (18no) saw the visitors to a victory target of 42 after Derbyshire had been dismissed for 219 in their second innings.
Derbyshire, 11 runs ahead overall on 189-7 overnight, lasted less than eight overs while adding a further 30 to their total on the fourth morning before being all out.
James Anyon (3-46) had Richard Johnson caught at fine-leg for 16 and his fellow seamer Steve Magoffin claimed the last two wickets, Tim Groenewald and Mark Footitt, for figures of 4-44.
That left Sussex a modest run chase and, despite losing Chris Nash caught behind cutting at Groenewald for a first-ball duck in the third over, second-wicket pair Wells and Yardy steered them over the line inside six overs with a flurry of boundaries.
The win, Sussex's second of the season, lifts them up to fourth in the Division One table, having played a game less than all of those above.
Derbyshire, who were promoted last season as Division Two champions, have lost four in a row and sit bottom of the table.