The Paris St Germain star struck three times in the opening 32 minutes in Boston as France maintained their 100 per cent record in Group I in the absence of coach Didier Deschamps.
Kylian Mbappe failed to register for the first time in the tournament but still crafted two assists in a sparkling performance that was capped by a late header from Desire Doue.
Norway made 10 changes, including leaving Erling Haaland and Martin Odegaard on the bench in a move that denied the audience a head-to-head between him and fellow Golden Boot contender Mbappe.
The Manchester City forward could only watch as Jorgen Strand Larsen had a penalty saved, but an outclassed Norway did at least get on the scoresheet with a fine effort from Rangers' Thelo Aasgaard.
France, for whom Guy Stephan was in charge following the recent death of Deschamps' mother, had no intention of easing up.
They almost led after 22 seconds when Mbappe smashed a shot against the underside of the crossbar. Egil Selvik got a fingertip to the effort before denying Jules Kounde and Manu Kone in quick succession.
The breakthrough came after just seven minutes as Mbappe's superb crossfield pass released Dembele, who weaved inside and out before firing home.
Norway threatened through Larsen, who controlled a high ball before shooting over, but Mbappe soon forced another save from Selvik.
Mbappe created Dembele's second in the 20th minute by shrugging off Leo Ostigard before picking out the winger, who cut inside and curled a superb effort beyond Selvik.
France had barely finished celebrating when Norway replied. Andreas Schjelderup released Aasgaard, whose body swerve wrong-footed two defenders before he fired past Mike Maignan.
Dembele completed his treble after a patient team move, once again cutting inside to curl a shot into the far corner.
France almost had a fourth when Doue pounced on a poor backpass but could not get around Selvik.
Norway were handed a route back into the contest when Oscar Bobb was fouled by Theo Hernandez, but Larsen's tame penalty was pushed away by Maignan.
Mbappe continued his search for a goal but fired over before being withdrawn late on as France advanced to the last 32 in style.
Bobb could have set up a grandstand finish but shot straight at Maignan before Doue had the final say.
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