Durham 274 for 8 (Richardson 64, Coughlin 62*, Tahir 5-98) trail Derbyshire 368 (Critchley 102, Godleman 98, Madsen 54) by 94 runs
The South African, who is playing for his sixth county, celebrated by sparking the decline that saw Durham lose 4 for 18 in 43 balls either side of tea before the visitors rallied to avoid the threat of following-on.
Derbyshire controlled the game for much of the day with Billy Godleman falling two shot of a century as he and Gurjit Sandhu took their 10th wicket stand to 102 before the home side were bowled out for 368.
Durham were going well at 119 for 1 but after Jack Burnham played on to Tahir and 16-year-old off-spinner Hamadullah Qadri bowled Michael Richardson for 64, the visitors crumbled before Paul Coughlin with an unbeaten 62 and Barry McCarthy guided them to 274 for 8, 94 behind.
Derbyshire’s first objective at the start of the day was to get to a fourth batting point which was achieved after a 35-minute rain break with Godleman and Sandhu frustrating the bowlers for another 15 overs before Godleman was caught behind hooking at Coughlin.
Sandhu followed his unbeaten career-best 48 by taking the new ball but Richardson and Cameron Steel added 52 before a mix-up saw Steel run out for 21 in Tahir’s first over.
The legspinner’s second over gave no indication of what was to come as Richardson dispatched him for two fours before Burnham drove him over extra cover for six.
But when Burnham tried to whip a ball from off stump and chopped on, Durham’s hopes of a decent reply faded as Qadri followed his record-breaking five-wicket haul at Cardiff last week by beating Richardson in the flight.
Paul Collingwood was bowled pushing forward at Tahir in the first over after tea, Ryan Pringle was lbw playing back to one that sung in from Sandhu and Graham Clark was the sixth to go with Durham still 205 behind.
The threat of the follow-on loomed when Stuart Poynter sliced a drive to point and Tahir bowled Matthew Potts with the next ball but Coughlin and McCarthy denied Tahir to keep Durham in the contest.