Duanne Olivier notched a second five-wicket haul to finish with match figures of 10-125, but Durham took four quick Derbyshire wickets to leave the visitors on 69-4, chasing a further 199 runs to win.
The South Africa quick (5-105) struck early, but Gareth Harte (114) led the Durham resistance with a maiden first-class century to frustrate the Derbyshire bowlers and help Durham to 376 all out after being 155-6 overnight.
Matt Salisbury (2-16) and Chris Rushworth (2-22) ran through the Derbyshire top-order as the hosts seized the advantage, but Ben Slater (41 not out) remains for the visitors, who face a tough test on the final day at Emirates Riverside.
Olivier had Cameron Steel caught behind for six early in the morning session, but that is when the Durham fightback started as Nathan Rimmington joined Harte at the crease to start an eighth-wicket partnership which eventually totaled 104.
The former Derbyshire bowler hit 42 off 75 balls, including five fours, before he was lbw to Matt Critchley with the score 263-8 as the lead past 150.
Olivier and Hardus Viljoen looked to wrap up the Durham innings with the new ball after lunch, but were met with further stubborn resistance from Harte and debutante Salisbury.
25-year-old Salisbury faced 147 balls for his gritty 25 as the pair put on 99 for the ninth wicket, batting throughout the second session as Derbyshire toiled but were often wayward in their pursuit of wickets.
The stoic Harte registered his first century in the format as the lead increased to 250, before Olivier had his fifth of the innings and tenth of the match when he bowled Salisbury.
Harte was eventually out three overs later, caught by Critchley off Wayne Madsen for a well-made 114 as Durham set Derbyshire 268 runs to win and up to 29 overs to face on Day Three.
Buoyed by their batting performance, the Durham bowlers started brightly, reducing Derbyshire to 35-4 as Salisbury bowled Godleman (10) and had Madsen (0) caught and bowled in the same over.
His fellow opening bowler Rushworth then struck twice at the other end, Alex Hughes (4) and Critchley (0) both lbw to consecutive deliveries.
Slater showed resistance for Derbyshire and closed on 41 not out, alongside Callum Brodrick, who will resume the final day on nine, with Derbyshire needing 199 more runs to win.
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