Sinner has been the dominant force on indoor hard courts, with this his 27th victory in a row on the surface.
His serve was superb in a high-quality first set. He won 24 of 27 first-serve points, did not lose a single point behind his first serve and did not face a break point.
Auger-Aliassime took a set off Sinner during his run to the US Open final and hit hard from the off, rushing Sinner and occasionally matching him shot-for-shot.
But the injury at 6-5 30-0 up had an immediate impact, with Auger-Aliassime struggling to move and sending his shots long as he tried to hit his way out of trouble.
Sinner, who was taken to deuce just once in 10 service games, did not let up and sealed victory with an ace before being serenaded by his home crowd.
He and rival Alcaraz are in contention for the year-end number one ranking in Turin.
Sinner must defend his title – and hope Alcaraz loses a group match and does not reach the final – to retain the top ranking.
Alcaraz, in the opposite group to Sinner, began his campaign with a straight-set win over Alex de Minaur on Sunday.