A maiden five-wicket haul by Nathan Buck (5-68) had rounded off the hosts' innings for 281 early on day two.
Northants openers Duckett (53) and Rob Newton (50) put on 101 before Derbyshire seamer Will Davis (4-55) helped reduce the visitors to 171-8.
A half-century stand by Max Holden (68) and Buck (43) saw them close on 291-9.
Buck eventually fell lbw to Jeevan Mendis but Holden, on loan from Middlesex, remained at the crease at the close and registered his second career half-century in only his third match to give Northants a lead of 10 runs.
England batsman Ben Duckett made a half-century for Northants, before his side recovered from a first innings collapse against Derbyshire.