Collins, the runner-up last year to Ash Barty and seeded 13th, battled a left knee injury while defeating Anna Kalinskaya 7-5, 5-7, 6-4.
Pegula and Gauff could meet in the semifinals, while Collins could play No. 1 Iga Swiatek in the fourth round.
A quarterfinalist in Melbourne in each of the past two years, Pegula needed just 59 minutes to get past the 161st-ranked Cristian, who was appearing in her third Grand Slam event.
"Always feels good when you win a match like that. I think when those days come, you just kind of take it and don't complain and don't critique. You kind of just move on to the next one."
Gauff, who reached her first Grand Slam singles final at the French Open last year, was given the honor of opening proceedings on Rod Laver Arena and dominated Siniakova in the first set.
The Czech player led 4-2 in the second set, but Gauff rallied and clinched victory on her seventh match point.
"I was not expecting to open the tournament on Rod Laver," Gauff said. "I'm super-honored that the tournament chose me and Katerina. I'm really pleased with myself. Katerina's a fighter. I knew she was going to fight for every point. I just stayed strong mentally."
Collins required a medical timeout for a left knee issue early in the first set of her match with Kalinskaya but survived to win in just over three hours.