Russian world number 50 Khachanov, who lost the opening match in his three US Open tune-up events, was far from spectacular but did enough on a day when his Canadian opponent's energy level appeared to drop as the match wore on.
"I saw that maybe he had some physical issues ... it's part of our sport," Khachanov said during his on-court interview. "I wish him, let's say, to feel better, speedy recovery if he's injured; I don't know.
"What I can say from my side is I tried to give my best performance, fighting, fighting. I'm super happy to get this win."
The result meant Khachanov has now reached the third round of all four Grand Slam tournaments in a single calendar year for the first time.
Khachanov, who made a run to the US Open semi-finals in 2022, broke Auger-Aliassime's serve seven times on the Louis Armstrong Stadium court and saved seven of the nine break points he faced en route to securing only his second top-10 win at a Grand Slam.
Auger-Aliassime looked ready to whip through the first set after consolidating a break for a 3-0 lead but was suddenly undone by a string of errors, allowing Khachanov to pull ahead before the Canadian broke for a second time to get to 4-4.
But Khachanov showed he was ready for a fight and twice held at love while serving to stay in the set before falling short in the tiebreaker, which ended when he sent a backhand long after chasing down an Auger-Aliassime volley.
In the second set, it was Khachanov's turn to jump ahead 3-0, but he never looked back, ultimately closing it out on his serve after coming back from 15-40 down.
Khachanov cruised through the third set, breaking at love to reach 4-1 en route to wrapping up the frame on his serve and leaving Auger-Aliassime with a long road back on a day when little was going right for him.
The Russian, displaying full confidence in his swings, wasted little time in the fourth set, opening up a 4-0 lead that appeared to drain the energy and strength from Auger-Aliassime, who looked a shell of his normal self.
Khachanov went on to close out the encounter with a four-point hold, the final blow coming with a massive serve that Auger-Aliassime failed to return.
Up next for Khachanov, who has only reached two quarter-finals this year, will be either Frenchman Benjamin Bonzi or Peruvian 32nd seed Ignacio Buse.