Tsitsipas, who was beaten in the Australian Open final by Novak Djokovic, took just over an hour and a half to beat Finnish player Emil Ruusuvuori 7-5, 6-1.
The Greek, ranked third in the world, next faces the winner of Wednesday's match between Jannik Sinner and France's Benjamin Bonzi.
Tsitsipas admitted he had initially struggled to find his groove.
"I had an opportunity in the last game (when Ruusuvuori led 5-3) to come back. I revived from that, I regenerated some awesome tennis and I recaptured that first set, which was crucial," he said.
"I think from that point onwards it was flawless tennis. I was able to produce some really good shots."
Auger-Aliassime, the third seed in Rotterdam, had no problem in dispatching the Italian Lorenzo Sonego 6-2, 6-3 as he hit his stride in the tournament where he beat Tsitsipas in the final last year.
In the next round the 22-year-old Canadian must overcome another French player, Gregoire Barrere, who eliminated David Goffin in the first round.
Poland's Hubert Hurkacz, ranked number 10 in the world, defeated veteran Spaniard Roberto Bautista Agut in a three-hour contest.
Alexander Zverev, still on the comeback trial after suffering an injury in the French Open last year, overcame South Korea's Soonwoo Kwon 6-4, 7-6 (7/4).
