Fynn Hudson-Prentice claimed his maiden first-class wicket on a third successive challenging day for bowlers at The Pattonair County Ground.
The all-rounder picked up the wicket of Max Holden with his first ball in Derbyshire whites, to leave the visitors 204-5 which soon became 250-6.
But an unbroken 186-run sixth wicket stand between Dawid Malan (177 not out) and John Simpson (91 not out) took Middlesex beyond the follow-on target and to 436-6 at the close, trailing by 121 runs.
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