Auger-Aliassime quickly found himself 4-1 down in the first set, with Shelton putting the serve and volley to good use, but he broke back as his opponent served for the set.
However, a poor service game handed the initiative – and the opener – to fifth seed Shelton.
Shelton had the only break point of the second set but an increasingly confident Auger-Aliassime saved it, before clinching the tie-breaker on a wild double fault from Shelton.
A tight third set was also decided on the Shelton serve, with Auger-Aliassime converting his third match point.
“He was playing much better than me at the start,” Auger-Aliassime said.
“It was a weird start, but as the match went on I was finding ways to put returns in the court.”