In a battle of the tour's young guns, 58th-ranked Auger-Aliassime came out firing, and the 18-year-old's aggression paid off with a victory over 20-year-old Tsitsipas, who shot to prominence in January with a victory over Roger Federer at the Australian Open.
Tsitsipas was coming off a runner-up finish to Federer in Dubai, where the Swiss great claimed a remarkable 100th career title.
Tsitsipas's Dubai run, which included an epic semi-final victory over Gael Monfils, saw him enter the world top 10 for the first time.
But he could find no answer to Auger-Aliassime, who broke early in the first to gain the upper hand and seized a 2-1 lead with the first of two breaks in the second.
After fighting off six break points in the opening frame, Auger-Aliassime saved another to seize a 4-2 lead in the second. He then broke Tsitsipas at love to give himself a chance to serve for the match and put it away with a service winner.
"It's unbelievable," Auger-Aliassime said. "I never expected to play that well today, to get my first top-10 win is special, against Stefanos who has been playing so well."
Tsitsipas admitted he was feeling the effects of his recent deep tournament runs.
"My mind at the moment is not very fresh," he said, but added that Auger-Aliassime "deserves every single piece of that victory.
"It seemed like he was really pumped and really energized today," Tsitsipas said. "He has kind of a strange tempo in his game, and you always feel like he's going to hit very hard, but then you don't really know what to expect, how hard he's going to hit the ball. So you're always caught out of position."
Auger-Aliassime, who will next play either Japan's Yoshihito Nishioka or Spaniard Roberto Bautista Agut, is one of four teens in the draw, along with countryman Denis Shapovalov, Alexei Popyrin and lucky loser Miomir Kecmanovic.
Kecmanovic gained entry into the second round in place of injured fifth-seed Kevin Anderson.
He made the most of his chance, beating Germany's Maximilian Marterer 6-3, 6-2 to reach the third round.
Later Saturday, world number one Novak Djokovic opens his campaign for a record sixth Indian Wells title against US qualifier Bjorn Fratangelo.
Djokovic, playing his first tournament since lifting his seventh Australian Open trophy in January, is hoping to pick up where he left off in Melbourne.
Last year, Djokovic was still feeling his way back in the wake of elbow surgery when he lost his Indian Wells opener to 109th-ranked qualifier Taro Daniel.
He returns back atop the world rankings after having won the last three Grand Slams.
Third-seeded German Alexander Zverev is also in action, kicking off his bid for a fourth Masters 1000 title against Slovakian Martin Klizan.