Musa's goal gave the Super Eagles a two-point lead at the top of Group F as closest rivals Malawi were earlier held to a goalless draw by Namibia at home in Blantyre.
Nigeria, who are heading to the Confederations Cup in Brazil later this month, moved on to eight points with two games to play as Malawi failed to keep pace.
Nigeria visit Namibia next Wednesday while Malawi host Kenya at the same time in another crucial round of matches with only the group winners progressing to the third qualifying round.
It was Nigeria's first win since they unexpectedly triumphed at the African Nations Cup in South Africa in February.
They needed an equaliser in added time at home to Kenya in March to avoid a major setback on the road to Brazil and drew 2-2 with Mexico in a friendly last week before travelling from Houston, Texas to Nairobi for Wednesday's World Cup qualifier.