Worcestershire 237 and 70 for 2 trail Derbyshire 578 for 5 dec (du Plooy 238*, Dal 141*) by 271 runs
Derbyshire's mammoth total of 578 for 5 declared was their highest against Worcestershire and earned them a first innings lead of 341.
Dal also emulated his achievement of in the corresponding game last summer of scoring a century and taking five wickets in an innings.
Du Plooy was unbeaten on 238 and his marathon knock spanned nine hours and contained two sixes and 25 fours.
Dal ended on 141 not out from 193 deliveries with five sixes and 13 fours when the declaration came mid-way through the afternoon session.
Worcestershire were left to reflect on a below-par bowing performance, with only Joe Leach emerging with much credit, and a slipshod fielding display.
Derbyshire will have aspirations of chasing a first Championship victory in 10 games stretching back to when they recovered from 14 for 5 on the opening morning to defeat Worcestershire at New Road last summer.
Their bowlers then made early inroads with Jake Libby and Azhar Ali falling cheaply as Worcestershire reached 70 for two before bad light ended play with 16 overs remaining.
Derbyshire resumed on 374 for 5 and Dal survived a chance to Josh Baker at second slip off Leach before he had added to his overnight 20.
Du Plooy went past his previous first-class best of 186 for South Western Districts versus Northern Cape at Kimberley in February 2022 when he cut Navdeep Saini for four.
The 28-year-old is certainly in prime form after over-taking his Derbyshire best of 170 against Yorkshire at Chesterfield earlier this month.
He went onto become the first Derbyshire player to score a double hundred at New Road and a late cut for four off Saini took Dal to three figures.
Worcestershire were powerless to halt the onslaught before du Plooy called a halt to the Derbyshire first innings and then his bowlers went to work.
Stand-in captain Libby went for a pull to the first delivery from Luis Reece and keeper Brooke Guest ran around to deep backward square to hold onto a skier.
Azhar Ali survived 33 deliveries for just three runs before he tried to work Nick Potts to leg and was lbw.
There was just time for debutant Rehaan Edavalath to get off the mark - after his first innings duck - before the light closed in with Gareth Roderick unbeaten on 38.