The winger created goals for James Collins and Sam Vokes before adding a magnificent third himself.
The hosts opened the scoring in the 12th minute when Bale whipped in a dipping free-kick from the right and Collins rose to plant a header past Hannes Halldorsson.
Bale tested the goalkeeper twice before Iceland equalised in the 26th minute when Johann Gudmundsson's shot deflected into the Welsh net off their captain, Ashley Williams.
Bale continued to run the show and, in the 63rd minute, he raced on to a long ball from Williams and charged into the Iceland box.
His shot from a tight angle was blocked on the line by Rotherham's Kari Arnason but Vokes was on hand to head home.
Seven minutes later, Bale made a surging run from inside his own half, bypassing two challenges before cutting on to his left foot inside the box and drilling home a low shot.