Wayne Madsen hit his 27th first-class century for Derbyshire, but Northamptonshire closed on 174-3, chasing a further 140 runs to win.
Alongside Matt Critchley (51), Madsen batted fluently and with purpose as he guided Derbyshire to 342 all out to set the visitors 314 runs to win at Queen’s Park.
Dan Wheeldon (1-12) struck early in the chase, and there were wickets for Critchley and Hamidullah Qadri, but Alex Wakely (48 not out) and Richard Levi (unbeaten on 22) closed with their partnership standing on 51 and Northamptonshire needing 140 more runs to win.
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