Ighalo who was top scorer in the qualifiers with seven goals netted the winner 13 minutes from time.
The Super Eagles dominated the opening exchanges with young winger Samuel Chukwueze causing problems for the Burundi defenders.
It was however Burundi who carved out the first real chance of the game with Cédric Amissi getting behind the Nigerian defence but his well struck shot was saved by Daniel Akpeyi.
Paul Onuachu who was preferred ahead of Ighalo to lead Nigeria’s attack had a number of attempts at goal but failed to beat Burundi goalkeeper Jonathan Nahimana.
Frédéric Nsabiyumva came close to handing Burundi the lead in 31st minute but we’ll placed header hit the upright.
Nigeria were forced to make a substitution when Chidozie Awaziem took the place of the injured Shehu Abdullahi three minutes from time.
Burundi gained in confidence after the break and took the game to the Super Eagles but were unable to break down the defence.
Nigeria head coach Gernot Rohr introduced Ahmed Musa for John Mikel Obi in the 56th minute in a bid to add more urgency to his side’s play.
The move paid off as the Super Eagles pinned their opponent back and created a number of half chances.
The breakthrough came in the 77th minute when Ighalo slotted the ball home after receiving a beautiful pass from Ola Aina.
The Super Eagles held on to the lead despite late charge by the Burundians.
The three-time champions will face the Syli National of Guinea in their next game on Wednesday.