The 36-year-old pace bowler claimed his 500th first-class wicket after making a career-best 87 off 167 balls in Leicestershire’s imposing 528 all out.
Lewis Hill scored 113 from 174 balls and Harry Swindells 76 with seamer Ben Aitchison taking 3 for 71 from 28 overs.
Spinners Matt Critchley and Alex Thomson each took three wickets but Derbyshire need 378 just to avoid following-on and ended day two in deep trouble on 41 for 3.
Leicestershire’s aim from the start of the day was clear as Hill and Wright accumulated steadily without taking risks.
Hill completed his second championship century of the season with a scampered single to mid on and the stand with Wright was worth 82 in 25 overs before Derbyshire broke through.
Aitchison was rewarded for an excellent spell from the Racecourse End in which he found some movement and bounce with wickets in consecutive overs.
Hill was beaten by one that lifted and seamed away before Louis Kimber edged behind as he pushed forward.
Wright, who was reported for dissent in the previous match, had nothing to complain about this time as he drove Critchley for six before another boundary off the leg-spinner took him past his previous best first-class score of 77.
His chances of a maiden hundred disappeared when he was stumped coming down the pitch to Thomson but Swindells and Ben Mike scored almost at will to take Leicestershire to 475 for 6 at tea.
Leicestershire pressed on after the interval, losing Mike to a diving return catch by Critchley and Swindells who drove Thomson to wide long on.
Callum Parkinson and Ed Barnes both fell trying to clear the ropes leaving Derbyshire a potentially awkward 20 overs to negotiate before the close.
After almost two full days in the field, it was always likely to be a difficult period for the openers and Wright’s landmark dismissal came when he had Tom Wood caught behind off a lifting delivery.
Former Derbyshire seamer Will Davis found late movement to remove Leus du Plooy and Wayne Madsen edged another lifter to give Swindells his third catch to leave the home side with a lot of work to do to avoid defeat.