Ben Slater top-scored with 68, but Derbyshire failed in their final day chase and lost to Durham by 95 runs at Emirates Riverside.
The Derbyshire opener batted resolutely, but wickets fell at regular intervals throughout the innings and the visitors were eventually all out for 172, confirming a 95-run win for Durham.
Resuming on the morning of day four on 69-4, needing a further 199 runs to reach their target of 268, Derbyshire lost Callum Brodrick (19) in the third over, caught behind off Rushworth.
Daryn Smit was lbw to Matt Salisbury in the next over for one, all but ending Derbyshire’s hopes of a final day fightback.
Slater continued to bat well and the 26-year-old reached his fourth-half century of the campaign off 93 balls with three fours.
His determined knock was the only one of substance for Derbyshire, but the opener was eventually out to a seaming delivery from Salisbury as Durham closed in on victory.
Tony Palladino (29 not out) and Duanne Olivier (18) showed lower-order resistance, but the South Africa quick was last man out as Rushworth claimed his fifth to seal a 95-run victory for Durham.
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