At 18, Auger-Aliassime became the youngest Queen's semi-finalist since Australia's Lleyton Hewitt at the same age in 1999.
However, Auger-Aliassime, who has risen to the cusp of the top 20 from outside the top 100 this year, said he is not thinking of achieving what 17-year-old Becker did in 1985 when he swept the Queen's and Wimbledon titles.
"Not really," the eighth seed said. "Honestly I had few expectations coming here but I have handled my nerves and I don't want to think too far ahead."
The Canadian may have been seeded lower, but he owns a perfect record against Tsitsipas with three victories as a junior and now two on the ATP Tour.
Auger-Aliassime explained that his rapid rise up the rankings this year is the fruit of a lot of hard work.
"I think this year I just kind of found my rhythm, I just found my beat, and I think I have been on the right track," he said.
"I haven't left sight of it. I think that's how I explain my rapid rise this year."
Tsitsipas, two years older than his opponent, admitted he is going to have to find a magic formula to beat the Canadian.
"He's the most difficult opponent I've ever faced, and I think it's gonna take a couple of tries to beat him," said Tsitsipas.
"It's upsetting obviously that he's better than me. I have to accept that he's better than me.
"I might never beat him, but if I think that way, just need to wait, years maybe, for that chance to come."
Tsitsipas, who joked he might donate $10 000 to charity when he does beat the Canadian, was not helped by a painful right shoulder which required on-court treatment.
His misery was compounded by two falls in the final game of the first set.
He said he woke up feeling sore and blamed it on having to play two matches on Thursday - an unfinished first-round clash with Kyle Edmund and then a tough three-setter with journeyman Frenchman Jeremy Chardy - although it was the same for Auger-Aliassime.
"Playing two matches wasn't easy," he said.
"Playing a three-set match was really difficult, not just for my nerves but also for my body. So that was it."
Auger-Aliassime will next play 37-year-old veteran Feliciano Lopez who became the oldest semi-finalist since 44-year-old Pancho Gonzalez in 1972 in coming from a set down to beat former Wimbledon finalist Milos Raonic 4-6, 6-4, 7-6 (7/5).
Fourth seed Daniil Medvedev became the first Russian to reach the last four at Queen's in the Open era as he outplayed Argentina's Diego Schwartzman, 6-2, 6-2.
Schwartzman's hopes of repeating his impressive win over defending champion Marin Cilic in the second round were quickly doused by Medvedev, who broke in the first game of the match and then in the fifth and then did the same again in the second.
The Russian will next face Gilles Simon who defeated French compatriot Nicolas Mahut 7-6 (7/5), 5-7, 7-6 (7/3).