Derbyshire 108 and 377 (Lace 132*, Palladino 58, Barnard 4-48) beat Worcestershire 113 and 290 (Ferguson 127, Cox 62, Rampaul 4-64) by 82 runs
Derbyshire secured their third Championship victory of the campaign to strengthen their promotion challenge despite a splendid century from Worcestershire batsman Callum Ferguson at Kidderminster.
The visitors bounced back in style after being bowled out for 108 on the opening day to claim 19 points and triumph by 82 runs.
Ferguson hit his maiden Championship hundred as Worcestershire showed plenty of resilience in recovering from the depths of 48 for 5 mid-way through the third day.
Worcestershire have now gone six games without a win since defeating Leicestershire and Durham in their opening two fixtures. They have paid the price for their batting frailties, with the exception of Ferguson, in the top order, where there has been a lack of consistency.
Worcestershire resumed on 156 for 5 with Ferguson unbeaten on 71 and Cox 44 not out with the second new ball due in 13 overs.
Runs flowed at a fast pace against the opening attack of Hudson-Prentice and Anuj Dal. Ferguson collected successive boundaries via a cut and a back-foot square drive at Hudson-Prentice's expense.
But, after playing so well, he had a slice of good fortune on his side as he raced towards three figures. Ferguson edged Fynn-Prentice and Dal for boundaries and a single off the former took him to his century off 205 balls with 17 fours.
Cox went to his half-century in the next over from Dal from 140 deliveries with eight boundaries.
The 150 partnership came up in 49 overs before the new ball was taken immediately at 206 for 5 off 80 overs.
Rampaul made the breakthrough for Derbyshire in his first over of the day. Cox, on 62, tried to get his bat out of the way of a sharpish Rampaul delivery but only succeeded in deflecting it onto his stumps.
Ferguson was joined by Brett D'Oliveira, a century maker in last week's game at Cardiff, and he cut Rampaul for four after the West Indies paceman changed ends.
Worcestershire reached 245 for 6 by lunch with Ferguson unbeaten on 126 but he added only one more after the resumption. Hudson-Prentice ended his fine knock by trapping him lbw. Ferguson's six-hour innings contained 20 boundaries and came off 267 balls.
D'Oliveira made an accomplished 30 before he was lbw to Palladino and the innings was quickly cleaned up thereafter. Dillon Pennington fell lbw to Rampaul for a duck and Joe Leach holed out to mid on off Palladino.