Aiming to maintain their perfect record in AFCON third-place play-offs, Nigeria were presented with the lead when Tunisia goalkeeper Moez Ben Cherifia and defender Yassine Meriah combined to tee up Ighalo.
Wahbi Khazri looked sharp as Tunisia rallied, and created his side's best chance when he set up Firas Chaouat for what should have been a simple finish early in the second half.
Chaouat could not take advantage, though, and while Ben Cherifia's excellent save from Samuel Chukwueze kept Tunisia's hopes alive, Nigeria had little trouble holding on to their lead.
Nigeria had the lead inside three minutes, Ighalo tucking home after Ben Cherifia and Meriah made a mess of Jamilu Collins' cross.
Tunisia responded well and would have been level had Ferjani Sassi's header not been cleared off the line.
Ighalo's game came to an end at half-time - the former Watford striker appearing to suffer a hamstring injury.
Khazri's superb throughball put Chaouat through on goal a minute into the second half, but with only the goalkeeper to beat, Tunisia's substitute lashed into the side netting.
Chukwueze's long-range strike looked to be creeping in just after the hour, but Ben Cherifia made a superb save at full stretch.
Ghilane Chaalali bundled himself into shooting range as full-time approached, though a weak effort wide of the upright was all he could muster as Tunisia ended their tournament with a whimper.