The 21-year-old backed-up his maiden hundred against Durham on Sunday with 133 from 207 balls out of Worcestershire’s 326 for 5.
Azhar Ali made 88 from 192 balls, adding 187 in 56 vers with Haynes to follow the 195 stand they shared to save the Durham match before Derbyshire hit back with the second new ball.
Sam Conners removed Haynes before a brilliant catch by Anuj Dal sent back Brett D’Oliveira five overs before the close.
Derbyshire’s decision to bowl first on a pitch tinged with green was possibly based on the amount of rain in Derby the previous day but apart from Suranga Lakmal, the bowlers struggled.
Worcestershire batter Ali said: “It was hard work to start with but we felt it was a very good cricket pitch so if you applied yourself you could get in.
“We are glad we got the partnership going, especially the way Jack batted, it was exceptional. It was a good day for us.”