Derbyshire 427 (Madsen 85, Godleman 61) and 1 for 0 trail Durham 520 (Poynter 170, Richardson 115, Palladino 4-87) by 92 runs
Poynter made his maiden championship century and Richardson scored his first in nearly four years as the pair shared Durham's highest ever sixth wicket stand of 278.
Poynter was eventually out for a career-best 170 but he and Richardson had completely transformed the game as Durham ended on 520, a lead of 93, and at the close Derbyshire were 1 without loss from two overs.
Derbyshire held all the cards at the start of the day when Durham resumed 312 runs behind and still 162 away from avoiding the follow-on.
When Cameron Steel went in the first over, caught at second slip off Duanne Olivier, Derbyshire must have sensed there was a chance to take complete control of the game but Graham Clark and Paul Collingwood gave the first indications of the fightback to come.
Collingwood responded to a painful blow amidships from Hardus Viljoen by hooking him for six and Clark reached his 50 with a straight driven four off the South African.
The pair had added 54 when Ravi Rampaul found some late movement to have Collingwood caught behind for 27 and in the next over, Clark was lbw to one from Tony Palladino that kept low.
Durham were now back in trouble but that was to prove Derbyshire's last success for as Richardson and Poynter first regrouped and then dominated on a pitch which had now flattened out.
Derbyshire had a chance to break the stand when Richardson was 33 and the total 224 but wicketkeeper Daryn Smit put down the edge off Olivier diving to his right.
It proved a big moment in the day and perhaps the match as the pair moved through the gears in the afternoon sunshine with Poynter completing his century from 128 balls as 148 runs came in the session.
Poynter cut Matt Critchley's leg spin for his 17th four to reach 150 which also took Durham past their previous highest sixth wicket stand of 249 between Gordon Muchall and Phil Mustard against Kent at Canterbury in 2006.
Richardson completed his first championship century since May 21st, 2014 in the next over and it was a surprise when Poynter played across a low full toss from Olivier and was lbw.
Palladino had Richardson lbw for 115 and finished with 4 for 87 but it is Durham who go into the final day on top.