Playing just nine days after his US Open semi-final defeat, Draper fended off two break points early in the first set and went toe-to-toe with Auger-Aliassime for the rest of the set.
Draper, 22, fought back from 6-3 down in the resulting tie-break, saving five set points before eventually conceding with a poor miss.
He responded by smashing his racquet furiously on the court floor which led to a leaf-blower being used to clean up the debris.
It looked promising for Draper when he broke in the first game of the second set but he was soon pegged back and paid the price when Auger-Aliassime struck again for a 6-5 lead, ultimately serving out victory with an ace.
It was Auger-Aliassime’s first win over Draper in three attempts – as well as being some payback for a controversial ending to their match in Cincinnati last month.
Auger-Aliassime argued Draper had pushed the ball into the ground before it went over the net and won him the match – something the umpire ruled was a legal shot, but the Briton faced criticism for not conceding the point.
“With what happened last time, I was just trying to get redemption,” Auger-Aliassime said on Sunday.
“Not to get into whether it’s his fault or the referee’s fault, but I had to go to bed knowing that the match wasn’t finished.”
Draper added: “I think it’s good in tennis to have rivalries and to have situations where not all tennis players get on massively. Hopefully we have many more battles to come.”
