Gnauduillet headed home Eoin Doyle's cross from the right in the 87th minute.
Darikwa then produced a super strike across Pompey keeper John Sullivan in the second minute of stoppage time to secure the Spireites' fourth win in their opening five League Two matches.
Pompey were reduced to 10 men seven minutes before the break when skipper David Connolly was given a straight red card by referee Stephen Bratt for an off-the-ball incident near the centre circle with Sam Hird.
After furious protests from the Chesterfield side, Bratt consulted assistant referee Michael Webb and then gave Connolly his marching orders.
Portsmouth defender Sonny Bradley came close with nine minutes remaining. He produced a furious charge into the Chesterfield box. Spireites stopper Tommy Lee could not hold his shot on goal, but he saved Andy Barcham's follow-up.
That was before Gnauduillet's header and Darikwa's clincher denied battling Pompey a share of the spoils.