Captain Harmony Chidi put the Flamingos ahead in the 16th minute before Awawu Bashiru doubled their advantage. Adegbuyi had a goal ruled out for offside before half-time.
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Nigeria continued to dominate after the break, with Niger Republic struggling to handle their pace and attacking movement.
Ohunene Sunday made it 3-0 in the 83rd minute before Mary Dunstan added a fourth shortly afterwards.
The Flamingos completed the emphatic victory with a fifth goal to begin their campaign in style. Nigeria controlled the game throughout, while goalkeeper Onyiyechi Opara had a quiet evening as the team secured a convincing opening win.