The opener, who hit 92 in the first innings, was 41 not out going into the final day and retired hurt with cramp after reaching 100 from 102 balls.
Roston Chase (60 not out) and paceman Kemar Roach (40 not out) added 104 before they declared on 327-6 at tea.
The hosts had reached 51 without loss at Derby when the draw was agreed.
Having decided to bat again on Saturday with a first-innings lead of 246, batting practice against the pink ball was the Windies' priority before Thursday's day-night Test at Edgbaston.
Only five batsmen had been required first time around, so Chase and the Hope brothers - who had all hit first-innings centuries - stayed down the order to give others time in the middle against Derbyshire's youthful attack.
But after Derbyshire opening batsman Charlie Macdonell - who had never previously taken a first-class wicket - removed both Shai and Kyle Hope in the space of three deliveries, it was the turn of Chase and tailender Roach to rack up the runs.
When the declaration came, it left Derbyshire an impossible target of 574 from one session under floodlights, so it was no surprise when the teams shook hands an hour later, at the earliest possible opportunity.
However, the Windies will again be concerned about the bowling form of pace bowler Shannon Gabriel, who had sent down 20 no-balls in nine overs in the first innings, and added four more in the four overs he bowled in the final session, giving him combined match figures of 2-88 from 13 overs.
Kieran Powell became West Indies' fourth centurion of their final warm-up game before the first Test against England, as they drew with Derbyshire.