The world number one was up a set and a break on Rod Laver Arena before faltering badly and slipping to a 4-1 deficit in the deciding set.
But she reeled off five straight games to win 6-4, 3-6, 6-4.
"Honestly I was at the airport already," a relieved Swiatek said in the immediate aftermath of her win in a match lasting more than three hours.
Ready to pounce
"I know she played perfectly but it was hard for anybody to keep that level so I wanted to be ready when mistakes came from the other side," she added.
"I'm really proud of myself because it wasn't easy.
"I felt like I had the momentum going and then she started to play suddenly two times faster and I had no idea how to react for a couple of games, but I came back and I thought the only thing I can focus on is myself.”
Collins beat 22-year-old Swiatek in the 2022 semi-finals in Melbourne, but the Polish top seed had won their past three meetings, which all came last season.
The American drew first blood in the contest, breaking in the fourth game for a 3-1 lead but folded to love in the next game as Swiatek got back on level terms.
The players were forced off court by rain with the score locked at 3-3 and 15-15, returning some 20 minutes later after the surface was mopped dry and the roof closed.
Swiatek broke again in the ninth game, drilling a backhand volley winner past Collins and served out for the set.
The top seed broke again in the first game of the second set to establish a firm grip, but Collins regrouped and reeled off five straight games.
Lost her nerve
The American, ranked 62nd in the world, lost her nerve at the crucial moment, serving four double faults to give Swiatek a glimmer of hope. But she got over the line in her next service game to level the match.
Collins raced into a 4-1 lead in the deciding set, with Swiatek unable to establish any sort of rhythm.
The Pole broke to love to reduce the deficit and then saved three break points in the following game to keep her hopes alive.
The pendulum had now swung and the top seed snuffed out any remaining chances for Collins to claim victory.
Swiatek will face unseeded Czech player Linda Noskova in the third round.