Shelton's service game powered him to win the opening set on Wednesday at the Inalpi Arena but Auger-Aliassime forced a decider with a tiebreak victory and converted a third match point to break the American's serve.
Both players had lost their opening round-robin matches, Shelton beaten by Alexander Zverev and Auger-Aliassime by defending champion Jannik Sinner and the chances of making the semi-finals now look bleak for the American.
"He was playing much better than me at the start. It's not often that I get broken twice in the first set indoors," Auger-Aliassime said. "It was a weird start, but as the match went on I was finding ways to put returns in the court.
"Once we engaged in the rallies, I felt like I could win more. You just have to fight, believe, and play the next point the right way."
The Canadian has now given himself a real chance of making the semi-finals with his win. He had needed medical treatment during his loss to Sinner, but he brushed off those worries this time even after Shelton stormed to a 4-1 lead in the opening set.
The American lost his cool when failing to serve out for the set, launching his racquet in frustration when Auger-Aliassime made it 5-4, but Shelton broke the Canadian again.
Shelton forced the only break point of the second set, but in the tiebreak Auger-Aliassime broke immediately to take a 3-0 lead.
The American hurt his knee when attempting a quick change of direction, limping through the rest of the tiebreak, but managed to save three set points before a double fault ended his valiant effort. Shelton didn't need any medical attention.
The Canadian held break points at 2-1 up in the final set but had to wait until the final game when Shelton was guilty of gifting match points, and Auger-Aliassime accepted gratefully.
"It was a weird start, but as the match went on I was finding ways to put returns in the court," Auger-Aliassime said.
"Once we engaged in the rallies, I felt like I could win more."Â
Sinner will face two-time winner Zverev in the other Bjorn Borg Group match later on Wednesday, where the Italian can secure a semi-final spot with a win, while the German needs a straight-sets victory to assure his last-four place.
