The 19-year-old Auger-Aliassime, who had his breakthrough season last year when he climbed up to world No. 17, nearly threw it away in the second set when he lost five games in a row before he regained his composure in the final set.
Fognini lost his focus following an argument with the umpire over a call in the second set, and the Italian also asked for the trainer’s help in strapping up his leg below the knee.
Khachanov sailed through the second set with two breaks of serve and Fognini’s unforced error count of 36 only made things easier for the Russian.
Meanwhile, Andrey Rublev knocked out Nikoloz Basilashvili 6-2, 6-3 in what was the shortest match of the first round, with the 22-year-old wrapping up the encounter in only 55 minutes after winning 91% of his first serve points.