Nadal must win the year-end title for the first time in his illustrious career to have a chance to avoid compatriot Carlos Alcaraz of the year as number one in the world, but he faded badly after an encouraging start.
The second-ranked 36-year-old was defeated by the American Taylor Fritz in his opener on Sunday and is bottom of the Green Group with one game to go against Norwegian Casper Ruud.
Nadal, the record 22-time Grand Slam champion, has now lost four consecutive ATP Tour matches for the first time since 2009.
Canada’s Auger-Aliassime, now coached by Nadal’s boxing uncle and longtime mentor Toni, will face Fritz in his final group game with a chance to make the final four.
“I had one game to get used to the conditions and I felt my game was better today, I hit it with precision and consistency,” Auger-Aliassime said on the court.
Nadal had the upper hand at times in the first set and twice threatened to break the serve of his opponent, who was defeated by Ruud on Sunday in his tournament debut.
Nadal served at 3-4 to lead 40-0, but a couple of double faults and some baseline errors allowed Auger-Aliassime to break.
Auger-Aliassime, who has won four titles this season, sealed the first set with a solid hold and moved a break ahead early in the second as Nadal stumbled trying to serve and volley.
Nadal has only played one tournament since the US Open and has looked well below his best.
He showed the occasional flash of brilliance, but failed to impress as he slumped to defeat, meaning he will be eliminated if Ruud wins against Fritz just one set later.
If that happens Alcaraz is confirmed as the youngest year-end number one since the introduction of the ATP rankings in 1973.