The result pushed the European giants to the top of the table with six points and five goals as they also beat Argentina in their second game while the Super Eagles are at the base with no point and minus two goals.
Musa showed superb technique to fire Nigeria ahead on the half-volley before the Leicester player rounded keeper Hannes Thor Halldorsson to make it 2-0.
Iceland gutted out a draw against heavily favored Argentina in Round 1 of Group D play.
This followed the 2-0 loss to Croatia in their opening game of the 2018 World Cup.
Nigeria coach Gernot Rohr made some tactical changes, including bringing Musa into the starting lineup to inject some pace into the attack.
U.S. envoy Nikki Haley berates human rights groups
Beyond the case of Israel, these same critics have called on the Geneva-based council to address its other glaring shortcomings. She had been threatening the pull-out since a year ago unless the council made changes advocated by the U.S.
Although the first half ended goalless, Iceland were the more purposeful side, with the Nigerians going into the break without a single shot on target.
British newspaper Daily Telegraph, in an appraisal of all the teams, rated Nigeria has only better than Saudi Arabia which lost the opening game of the competition 5-0 to host country Russian Federation and debutants Panama who lost 3-0 to Belgium. "However, we've moved past that disappointment and we're looking forward to the next game", Ndidi told FIFA's official website.
And on the stroke of half-time Finnbogason came within a whisker of doubling his World Cup tally when he flashed wide Gylfi Sigurdsson's whipped in free-kick.
But they missed the pace of winger Johann Berg Gudmundsson who was injured in the Argentina game. But Volgograd's heat, with temperatures around 30 degrees Celsius (86°F), sapped his team.