Khachanov won three straight games, taking the first set in 31 minutes.
The 30-year-old world number 26 kept his cool in chilly Beijing to break Auger-Aliassime on the first match point, wrapping things up in 1 hour 11 minutes.
He faces either Arthur Rinderknech of France or qualifier Alex Molcan of Slovakia in the round of 16.
"It was a tough match" despite his recent come-from-behind victory over 26-year-old Auger-Aliassime at the US Open, Khachanov said after his win.
"When you approach this match you are thinking it's a completely new match, completely different. In China, in Beijing. Different court, different balls," he said.
"You just focus again from zero. You know that what you did well... and you just try to keep the momentum going. There is not much secret about it."
Fan favourite Novak Djokovic of Serbia starts his bid to extend his perfect 29-match winning streak at the China Open, as he meets Nuno Borges in the first round Wednesday evening.
