After playing nine sets and more than 11 hours as he won his first three matches in the first-week heatwave, Auger-Aliassime sped through his fourth match in two hours, eight minutes with the temperature in the mid-20s.
"Today was the ideal scenario," said the Canadian.
"It was the best tennis I've played here. It's great than in the fourth match I've found my best tennis."
He will next play unseeded Italian Flavio Cobolli, and the Montreal-born Quebecker was keen to recruit the support of the Paris fans.
"This has always been a dream for me," he said on court. "I'm not French but I'm very Francophone, and I'm sure I can count on your support all the way to the end.
"I feel as if I'm at home."
The 25-year-old broke in the fourth game of the first set. He survived two break points as the Chilean attempted to fight back in the next game and then cruised to the set as the next four games were won to love on serve.
In the second set, Auger-Aliassime grabbed the only break he needed in the 11th game, and, as Tabilo subsided, raced through the third in 26 minutes.
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