The seven-time Africa champions returned to the Africa U-20 Cup of Nations after missing out of the 2017 edition staged in Zambia.
The Flying Eagles had the better chances of a close contest light on chances in Niamey, with the forwards’ pace causing plenty of problems for Burundi, who are making their second appearance in the championship.
Joslin Bipfubusa’s boys were unable to create a clear opportunity of their own and sit bottom of Group A following the first round of matches, South Africa and Niger Republic having drawn 1-1 earlier on Saturday.
After a cagey first half, Yahaya put Paul Aigbogun’s boys ahead with a powerful header in the 55th minute before Effiom doubled the lead in the 71st minute.
Nigeria face South Africa on Tuesday at the Stade General Seyni Kountche, Niamey – and victory for the west Africans will hand them a ticket to the 2019 U20 Fifa World Cup in Poland.