Ighalo, set free by Ola Aina's clever flicked pass, side-footed the ball past Burundi goalkeeper Jonathan Nahimana in the 77th minute, four minutes after coming on in the opening Group B match.
It was tough on Burundi who refused to be overawed and enjoyed slightly the better of the first half, with Frederic Nsabiyumva heading against the crossbar from a set-piece.
"We couldn't have produced a better performances because Burundi were very organised," said Nigeria coach Gernot Rohr.
"We knew Burundi were unbeaten in the qualifiers, and we knew the first matches would be difficult. These teams don't have anything to lose, they know us and know how to organise against us."
Fearless and uninhibited, Burundi gave as good as they got in an entertaining first half as they forced Daniel Akpeyi to make two difficult saves and hit the crossbar.
Cedric Amissi had Burundi's first chance when he latched onto a ball sent over the top of the Nigeria defence and unleashed a powerful volley which Akpeyi did well to block.
Akpeyi was also tested by Gael Bigirimana's swerving 30-metre free kick, before a looping Frederic Nsabiyumva header from a set-piece bounced off the top of the crossbar.
Nigeria were dangerous down the flanks with Samuel Chukwueze and Alex Iwobi although most crosses were cut out by the Burundi defence. Paul Onuachu was closest in the 14th minute with a header which forced a good save by Jonathan Nahimana.
Nigeria replaced captain John Obi Mikel with Ahmed Musa just before the hour in a bid to add to some speed to the attack but they continued to fail to make the final pass count.
However, one moment of inspiration settled the game. Aina wrong-footed the Burundi defence with his backheeled pass and left Ighalo to place a perfect finish wide of the goalkeeper.
(Reporting by Brian Homewood, editing by Ed Osmond and Tony Lawrence)
