The Super Eagles came into the match targeting three points after they suffered a 2-0 defeat to Bafana Bafana in their opening game.
The Seychelles, meanwhile, were embarrassed in their opening qualifier, going down 5-1 to Libya.
However, it was the visitors who got the first goal, with Ahmed Musa thumping home after being set up by Odion Ighalo after 14 minutes.
The second goal arriived in the 35th minute when Chidozie Awazeim slotted home from close range after Kelechi Iheanacho's free-kick hit the woodwork.
The Seychelles, on the other hand, struggled to carve out any serious attempts at Francis Uzoho's goal in the remaining stages of the first half.
Ten minutes into the second half, Nigeria got their third goal as Ighalo registered a goal to go with his assist, converting a penalty after Samuel Kalu was brought down in the box.
The hosts nearly pulled a goal back after the hour mark after an error from the Nigerian defence, but they were unable to take advantage.
That proved to be the Seychelles' only clear-cut opening as the Super Eagles managed to see out the remaining stages of the half with relative ease and claimed maximum points to get their qualification campaign up and running.