The tourists, 340-3 overnight, declared on 427-3 as Shai Hope (107) and Roston Chase (110) reached their centuries.
Captain Jason Holder (3-48) then led the way with the pink ball, which will also be used in next week's day-night Test against England at Edgbaston.
After Derbyshire were bowled out for 181, the Windies opted to bat again and were 60-1 by close of play at Derby.
Only teenager Calum Brodrick (52), on his first-class debut, and opener Ben Slater (39) passed 20 for the hosts.
The Windies' pace quartet - Shannon Gabriel, Kemar Roach, Alzarri Joseph and Holder - were all in the wickets as they warmed up for the first day-night Test to be held in England.
However, Gabriel, playing his first game of the tour, sent down 20 no-balls as his nine overs cost 64 runs.
Keeper Shane Dowrich had a busy day with five catches off the seamers as well as a stumping off Chase's off-spin when Brodrick was the eighth man out after adding 55 with stand-in skipper Tony Palladino.
West Indies had not registered a century in their first two tour games against Essex and Kent, which were both drawn.
But earlier in the day, Hope and Chase joined Hope's brother Kyle, Friday's centurion, in reaching three figures against an inexperienced county attack which included two teenagers and four others under 25.
Opener Kraigg Brathwaite, who fell cheaply for the second time in the match to give 16-year-old seamer James Taylor his maiden first-class wicket, will be the only West Indian to feel he missed out.
West Indies continued to dominate under-strength Derbyshire on the second day of their day-night tour match.