Having resumed on 127, Collingwood reached 177 before being caught at long leg to give Hardus Viljoen his fifth wicket.
Potts, who helped to put on 132, had added 40 to his overnight 13 when Durham declared on 480-9, to which Ben Slater and Luis Reece replied with 12 without loss in four overs to lunch.
Although Collingwood made 206 for England at Adelaide in 2006, his only higher championship scores both came in 2005 – 190 at Derby and 181 at Taunton.
He hit 20 fours in his 228-ball innings and pulled Viljoen for his only six the ball before he was out.
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Potts’ five previous first-class innings yielded three ducks, a two and 14 not out, but he looked assured on the placid pitch, even against the leg spin of Imran Tahir.
There were a couple of thick edges to the vacant third man boundary, but they were well controlled and he completed his 105-ball 50 with a fine shot through the covers off Tony Palladino.
Viljoen finished with five for 130, but once the shine had worn off the second new ball Derbyshire lacked the firepower to extract any life from the surface.