Three Derbyshire batsmen hit half-centuries as the hosts set Durham 361 runs to win in the final innings at The Pattonair County Ground.
Harvey Hosein (62), Tom Lace (61) and Matt Critchley (51) all surpassed 50 as the Derbyshire middle-order rallied to post 334 and set Durham a challenging chase.
Ravi Rampaul and Tony Palladino probed for a wicket in the final overs, but the Durham openers survived to reach 10-0 at the close.
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