Swiatek fought back from a double service break down in the deciding set to scrape into the last 32 with a 6-4 3-6 6-4 victory under a closed roof at Rod Laver Arena on Thursday.
A heavy shower midway through the opening set forced officials to complete the match indoors.
Fans could not have expected when play was briefly stopped at 3-3 what a roller-coaster three-hour, 13-minute encounter they would witness upon the match's resumption.
"Oh my God, I was at the airport already," the Pole said of her Houdini act from 4-1 down in the deciding set.
"But I wanted to fight till the end. I knew that she played just perfectly, but it would be hard for anybody to keep that level.
"So I wanted to be ready when more mistakes are going to come from the other side.
"And I just wanted to push her and I did that at the end and I'm really proud of myself because it wasn't easy."
Danielle Collins gave world No.1 Iga Swiatek a huge scare at the Australian Open. (James Ross/AAP PHOTOS)
After winning the opening set, Swiatek quickly found herself trailing 5-1 and 40-15 in the second.
She managed to fend off five set points before Collins finally levelled the match after some two and a quarter hours.
Swiatek, who lost to Collins in the semi-finals two years ago before Ash Barty stopped the feisty American in the title match, was staring down the barrel again after losing four of the first five games in the third set.
Collins, though, lost her nerve as the four-time grand slam champion dodged a bullet to extend her winning streak to 18 matches and remain on track for a maiden Open crown.
Presented with as devilish a draw as any top seed could expect, Swiatek also had to battle past 2020 champion Sofia Kenin in the opening round.
Alex de Minaur's girl Katie Boulter crashed out of the Australian Open in the second round. (Lukas Coch/AAP PHOTOS)
Rankings-wise, the four-time grand slam champion should find things a tad easier in the third round against Czech world No.50 Linda Noskova.
Noskova, a 6-3 1-6 6-4 winner over American qualifier Kessler McCartney, was among other players to progress on the weather-hit fifth day.
Chinese 12th seed Qinwen Zheng also marched on, eliminating Alex de Minaur's British girlfriend Katie Boulter 6-3 6-3.
Frenchwoman Clara Burel claimed the biggest scalp of her career with a 6-4 6-2 shellacking of American No.5 seed Jessica Pegula on Margaret Court Arena.
The 22-year-old caused the biggest boilover of the tournament to date in 70 minutes, having never beaten a top-10 ranked player in her five previous attempts.
Her third-round opponent will be compatriot Oceane Dodin, who led wire-to-wire in a 6-4 6-4 victory over Italian Martina Trevisan.
Former US Open champion Sloane Stephens took a page out of Swiatek's book to rally from a set down to see off Russian 14th seed Daria Kasatkina 4-6 6-3 6-3.
Sloane Stephens came back from a set down to book a spot in the last 32. (Joel Carrett/AAP PHOTOS)
Stephens next faces another Russian Anna Kalinskaya, a 6-4 6-4 winner over Dutchwoman Arantxa Rus.
Italian 26th seed Jasmine Paolini beat German world No.42 Tatjana Maria 6-2 6-3 and will play either Kazakh star Elena Rybakina, the 2023 Open runner-up, or Russian Anna Blinkova in the third round.
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