The result left both sides, and struggling Argentina, still in the hunt to go through from Group ‘D’ along with already-qualified Croatia.
But Argentina and World Cup debutants Iceland have to win their respective games against Nigeria and Croatia next week to have a chance of advancing.
In only the second win for an African side in Russia so far, Nigeria broke the deadlock in the 49th minute when Victor Moses, playing as a wing-back, lofted a pass towards Musa who deftly controlled the ball and smashed in the half volley.
Musa, recalled to the starting team by Coach Gernot Rohr, made it 2-0 in the 75th minute when he found space on the left, beat Iceland defender Kari Arnason and rounded goalkeeper Hannes Por Halldorsson before slamming the ball into the net.
Iceland, roared on by thousands of fans from the tiny country, kept pushing and were awarded a penalty in the 80th minute when Referee Matt Conger used the Video Assisted Referee system to confirm that striker Alfred Finnbogason had been fouled by Tyronne Ebuehi.
But Iceland's playmaker Gylfi Sigurdsson blasted his effort high over the bar.
The win vindicated the decision of Rohr to overhaul his attack after a limp 0-2 defeat to Croatia in Nigeria's opener, bringing in Musa and Kelechi Iheanacho at the expense of strikers Odion Ighalo and Alex Iwobi.