Daryn Smit hit 45 not out as Derbyshire posted 427 in the first innings before Durham closed on 115-2, still trailing by 312 runs at The 3aaa County Ground.
Resuming on 301-4, Derbyshire continued to find runs throughout the order as Matt Critchley (64) became the fourth batsman to reach a half-century and Smit added an unbeaten 45 before Derbyshire were all out for 427.
Hardus Viljoen (2-15) struck twice in the Durham reply, but Graham Clark (42 not out) and Cameron Steel (31 not out) saw out the remainder of the day as Durham closed on 115-2.
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