Having gone down 2-0 to Croatia in their first game, Nigeria would have joined African rivals Egypt and Morocco in exiting the tournament early if they had lost here.
They started slowly, becoming the first team in Russia not to have a shot in the first 45 minutes.
Yet they were a different proposition after the interval as they went on to secure only a second win in 14 games at a World Cup finals.
Musa, who ended last season at CSKA Moscow on loan from Leicester City, proved the difference having been recalled to the team after the Croatia defeat.
He showed exceptional quality to open the scoring, controlling a cross by Victor Moses before lashing home from 10-yards.
Having scored one of the goals of the tournament, Musa then hit the bar before scoring his second after Iceland’s defence had gone walkabout.
Nigeria still have to beat Argentina to make sure of extending their stay in Russia but this performance, particularly in the second half, will give them a huge lift for Tuesday’s group finale.
Nigeria’s last game of the group phase is against Argentina in St Petersburg on Tuesday (19:00 BST) while Iceland face group leaders Croatia in Rostov-on-Don at the same time.