Lionel Messi's team were pushed to the brink of an early exit after a stunning 3-0 loss to Croatia on Thursday, but victory in their final Group D game against Nigeria could now send them through to the last 16.
Musa was left out of Nigeria's loss to Croatia but he justified his recall to the side with the opening goal shortly after the interval at the Volgograd Arena on Friday.
The forward controlled a cross from Victor Moses and thumped an unstoppable drive into the roof of the net, with Musa becoming the Super Eagles' top scorer in the history of the tournament courtesy of his third World Cup goal.
Nigeria were poor in the first half - failing to record a single shot - but they were much improved after the break, Musa adding another to his personal tally in the 75th minute as Iceland's rock-like resilience crumbled.
Iceland, who saw Gylfi Sigurdsson miss a late penalty, need to win to stand any chance of making the knockout stages, although even three points may not be enough depending on the outcome of Nigeria's clash with Argentina with all three teams still standing a chance to join Croatia in the last 16.
Gylfi Sigurdsson had tested Francis Uzoho with an early free-kick as Iceland made a bright start.
Iceland's star man then fired a sixth-minute chance straight at the teenage goalkeeper, who dealt with a string of corners as both sides struggled for fluency in midfield.
But Iceland almost took the lead in the last minute of the first half, Alfred Finnbogason unable to get a decisive touch on Gylfi Sigurdsson's dangerous free-kick delivered from the right wing.
Nigeria, in contrast, were unable to put any cohesive attacking moves together, meaning they became the first team at Russia 2018 to fail to record an attempt in the first half
They did test Hannes Thor Halldorsson just 14 seconds after the restart, with the goalkeeper easily saving from Oghenekaro Etebo, who had scored an own goal in his team's 2-0 defeat in Kaliningrad at the weekend.
However, the Super Eagles opened the scoring with their next attack in the 49th minute.
Moses led a rapid break down the right with his cross brilliantly collected by Musa, whose superb first touch took defender Ragnar Sigurdsson out of the equation. If Musa's first touch was good his second was even better, a lashed finish on the half-volley giving Halldorsson no chance.
Nigeria's confidence levels grew in the wake of the goal, Halldorsson having to be alert to tip over a deflected rifled drive from Wilfred Ndidi.
Musa rattled the crossbar as Nigeria pushed to seal all three points - and the striker would not be denied again in the 75th minute.
Fed by Kenneth Omeruo, Musa burst clear in the left channel, cut inside and slipped a calm finish past Halldorsson.
Nigeria survived a late scare after a VAR review spotted substitute Tyronne Ebuehi had tripped Finnbogason, with Gylfi Sigurdsson's spot-kick effort clearing the crossbar.
But a late injury to captain John Obi Mikel, who appeared to hurt his hand during six minutes of additional time, could be a concern for Gernot Rohr's side ahead of an all-or-nothing clash with Argentina.
Key Opta stats:
- All six of Nigeria’s World Cup wins have come against European opposition, and they have kept a clean sheet in five of those victories.
- This was Iceland’s first defeat in a group stage match at a major international tournament, having previously drawn three and won one of their four games.
- Ahmed Musa has scored each of Nigeria’s last four goals at the World Cup, having also bagged a brace in a 3-2 defeat to Argentina in 2014.
- Gylfi Sigurdsson fired in two shots on target in the first six minutes of this match, as many as his side managed in total in 90 minutes against Argentina
- This was only Nigeria’s second win in their last 14 matches at the World Cup (D3 L9), having also beating Bosnia and Herzegovina in 2014.