Tom Lace scored his second first-class century for Derbyshire, while Wayne Madsen hit 60 as the visitors moved into a commanding position on Day Two.
After 20 wickets fell on Day One, Lace spent more than five hours at the crease on Day Two, finishing on 101 not out at Kidderminster.
He will resume with Fynn Hudson-Prentice, who is yet to score, as Derbyshire starting Day Three 272-6, leading by 267.
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