Musa (49th, 75th minutes) scored both his goals in the second half as Nigeria revived their chances of advancing to the second round.
The Africans, who had lost 0-2 to Croatia in their campaign opener, now have three points from two matches.
They now face a must win clash against Argentina in their third and last group encounter.
Iceland have two points from as many matches. They had held mighty Argentina 1-1 in their first match.
The result also helps the chances for Lionel Messi's Argentina to advance, as they can move from bottom of the table into second with a win over Nigeria, so long as Iceland do not beat Croatia by an equal or larger margin.
In the first half of the game, chances were few and far between. While Nigeria dominated possession, Iceland got the better chances to take the lead.
The best of them all was a Gylfi Sigurdsson effort which was tipped over the bar by Nigeria goalkeeper Francis Uzoho.
Nigeria nosed ahead four minutes into the second period when Victor Moses sprinted down the right wing and crossed towards Musa. The Nigerian controlled beautifully, before slamming home to give his side the lead.
Musa could have grabbed a hattrick had his attempt from 20 yards not come off the crossbar.
Musa then sped past Iceland right-back Kari Arnason on the wing to round goalkeeper Hannes Halldorsson and score his second of the evening.
Iceland were handed a lifeline when Tyronne Ebuehi was late on a challenge on Alfred Finnbogason, and the referee gave a penalty -- though only after reviewing the play on video.
But Sigurdsson sent his shot high over the bar and into the stands after a short run-up and Nigeria held on to take the three points.
(This story has not been edited by Social News XYZ staff and is auto-generated from a syndicated feed.)
