Arsenal winger Oxlade-Chamberlain ran riot in Reykjavik, scoring a quickfire first-half double before completing his treble shortly after the break.
The win maintained England's 100% start to their latest qualifying campaign, further banishing memories of the summer's dismal finals in Denmark ahead of Monday's trip to Norway.
The only negatives were hamstring injuries to Nathan Delfouneso and Martyn Waghorn, who both limped off and appear doubtful for the next game.
This was expected to be the first real test for Stuart Pearce's new-look side, who routed whipping boys Azerbaijan 6-0 in their opening qualifier last month.
Iceland had beaten England in their last meeting and had also reached this summer's finals, but it soon became clear their current crop of youngsters was not up to that standard.
The visitors quickly assumed control and could easily have gone ahead three times in the opening 10 minutes.
The returning Martin Kelly was denied by a fine save from Arnar Darri Petursson from Henri Lansbury's corner.
Lansbury then released Marvin Sordell down the right but the Watford striker made a hash of his finish on what was his full debut.
Kelly then narrowly failed to get his foot on another Lansbury corner but it was not long before England were in front as Oxlade-Chamberlain added to his burgeoning reputation.
The Arsenal winger pounced on a loose ball, raced goalward and coolly slotted home across the goalkeeper, who then gifted the 18-year-old his second three minutes later.
Petursson spilt Delfouneso's cross straight at the feet of Oxlade-Chamberlain, who passed the ball into the empty net.
The impressive Aron Johannsson did his best to get Iceland back into the game, while England were forced to replace Delfouneso with Waghorn in the 24th minute.
But they comfortably saw out the half and killed the contest within five minutes of the restart after more brilliance from the precocious Oxlade-Chamberlain.
The teenager easily beat two men before unleashing a cross-cum-shot from the tightest of angles which Petursson helped into the net.
Waghorn appeared to pull his hamstring on the hour mark and was carried off to be replaced by Josh McEachran.
England goalkeeper Jack Butland was finally called into meaningful action but it was a simple pouch of Johann Laxdal's header.
Oxlade-Chamberlain was withdrawn for the final eight minutes, with Everton midfielder Ross Barkley coming on.