Also Sunday, it was: Madagascar 1, Republic of Congo 0; and Angola 1, Togo 1; Ivory Coast 1, Congo (Zaire) 2; and Sudan 3, Sierra Leone 0.
On Saturday, Zimbabwe beat Malawi 1-0, and on Friday, Zambia beat Libya 4-2.
Victor Agali was the early hero for Nigeria, scoring the game-winning goal in just the first minute of the match. Agali headed in a free kick from Austin Okocha to put the Super Eagles on their way to their third straight World Cup finals.
Tijani Babangida followed with two more first-half goals, scoring in the 18th and 33rd minutes.
Supporters in Nigeria's soccer-mad commercial capital, Lagos, watched anxiously on television sets and took to the streets to dance after the game to celebrate.
Ghana's fate was all but sealed in the 41st minute, when goalkeeper Osei Boateng drew a red card for fouling a Nigerian attacker.
Boateng had arrived as a substitute just two minutes earlier, replacing first-string goalkeeper James Nanor. One of the Ghanaian forwards was forced to mind the net for the remainder of the match as his teammates withdrew into a defensive shell.
Nigeria won Group B with 16 points, one more than Liberia, which was hoping for a Nigeria loss or draw to give the West African nation its first World Cup final berth.
Sudan, with its win, is in third place in the group 12 points, followed by Ghana with 11 points and Sierra Leone with four.