Auger-Aliassime was in top gear as he dismantled his opponent, who looked out on his feet after beating Taylor Fritz on Wednesday in a slugfest, as well as coming back against Andy Murray in three sets before that.
The World No. 8 is in scintillating form after just winning three back-to-back titles, and he gave the 37-year-old no chance with his forehand dominating the occasion.
However, Simon got a wonderful reception throughout, and was given a special ceremony after the match to celebrate a great career, getting to two Masters finals in Madrid and Shanghai.
Auger-Aliassime will take on Frances Tiafoe in the quarter-finals, who battled past Alex De Minaur 6-3 7-6(5) - a day after the Australian had beaten Daniil Medvedev.
Meanwhile, young star Musetti fired 37 winners as he came from a set down to eliminate third-seeded Norwegian Ruud 4-6 6-4 6-4 and advance to his maiden ATP Masters 1000 quarter-final.
"He (Ruud) was playing really well and I had to play my best tennis to beat him. I am really happy that all the hard work I am doing keeps improving me. I am really proud of this win," said Musetti.
Musetti will take on Novak Djokovic for a place in the semi-finals after the Serbian, a six-times winner at the ATP Masters 1000 event, delivered a commanding performance in his straight-sets victory over Russia's Karen Khachanov, hitting 18 winners.
Top seed Carlos Alcaraz dominated Grigor Dimitrov 6-1 6-3, dropping just two points on serve in the opening set before fending off a second-set fightback from the Bulgarian to close out the match in one hour 12 minutes.
"(Grigor's) level is very much not the level you saw today, but I played very well," said Alcaraz, who is chasing a third ATP Masters 1000 title this season.
"At the end of the second set it was tougher for me, he came back, he raised the level and obviously it was tough. He had the chance to go up in the second set, I had to stay calm in that moment and show my best to not allow him to go up."
Alcaraz will play Danish teenager Holger Rune after the 19-year-old took down seventh seed Andrey Rublev 6-4 7-5.
Russian Rublev and Auger-Aliassime had secured their places at the season-ending ATP Finals in Turin on Wednesday.
Fifth seed Stefanos Tsitsipas served strongly to seal a 6-3 7-6(3) win over France's Corentin Moutet and reach the last eight.
The Greek will face either Spaniard Pablo Carreno Busta or American Tommy Paul who meet later on Thursday.
