Hardus Viljoen claimed 2-15 and despite a Durham fightback to close on 115-2, the visitors still trail Derbyshire 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 Daryn Smit added an unbeaten 45 before Derbyshire were all out for 427.
Viljoen 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.
Wayne Madsen (85) could only add five to his overnight score before he was lbw to Mark Wood as Durham took the new ball.
21-year-old Critchley reached his half-century off 63 balls but was spectacularly caught by Paul Collingwood in his follow-through, redeeming himself after earlier dropping the all-rounder off Wood.
He soon had Viljoen lbw to swing momentum back towards Durham, but Smit and Tony Palladino (29) proved to be a stubborn pair and added 62 valuable runs for the eighth wicket.
They took Derbyshire past 400 before Palladino was bowled by Steel and the leg spinner also had Duanne Olivier lbw without scoring.
Smit batted nicely for his 45 not out, his highest first-class score for the county, but he ran out of partners and once Ravi Rampaul was lbw to Matthew Dixon, Derbyshire were all out for 427 after adding 123 runs to their overnight score.
Steel and Aiden Markram (30) began the reply well and added 51 for the opening wicket, until Viljoen removed the South Africa opener and Will Smith (0) either side of tea to reduce Durham to 51-2.
Clark and Steel steadied the innings and took Durham past 100 in the face of good bowling from Viljoen, Olivier and Rampaul. Bad lighted forced the players off and brought an end to play with the score on 115-2, with the visitors trailing by 312 and Derbyshire still in a good position.
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