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.
While Swiatek avoided the scrap heap, third seed and last year's Open runner-up Elena Rybakina couldn't in an even more enthralling encounter with fellow Russian Anna Blinkova.
Rybakina saved an incredible nine match points but not a 10th as Blinkova prevailed 6-4 4-6 7-6 (22-20) in the longest tiebreaker in grand slam history, which stretched more than half an hour.
Blinkova herself fended off six match points.
"I will remember this match for the rest of my life," Blinkova said after booking a third-round date with Italian 26th seed Jasmine Paolini.
Latvian 11th seed Jelena Ostapenko, last week's Adelaide International winner, continued her fine run with a 6-0 3-6 6-4 victory over gallant local hope Ajla Tomljanovic.
Ostapenko will play what promises to be a blockbuster wth Victoria Azarenka in the third round after the Belarusian two-time champion repelled a tough challenge from Denmark's Clara Tauson, winning 6-4 3-6 6-2 after a two-and-a-quarter hour battle.
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.
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