Swiatek recovered well from her shaky second set to seal the win in one hour and 44 minutes, as she continued to build momentum in her hunt for a career Grand Slam.
The second-seeded Pole was at her ruthless best as she raced to a 5-1 lead with a double break and secured the opening set in only 24 minutes to turn the screws on an off-colour Kalinskaya, who received treatment on her lower back during the break.
But a role reversal in the second set saw six-time Grand Slam champion Swiatek drop serve three times as Kalinskaya controlled proceedings, capitalising on a number of errors off the Pole's racket.
Swiatek took a medical timeout between the second and third sets before returning with a vengeance, winning five straight games to stamp out Kalinskaya's resistance.
To her credit, the 31st seed was able to hold serve and made Swiatek defend three break points, but it was too little too late as the Pole held serve for the win.
Asked about the swings in momentum during the match, Swiatek said: "Honestly, it was not surprising for me ...
"I just wanted to be there when I have a chance, when I have a slower ball, to still be proactive and put pressure on her. I didn't feel like I was playing worse in the second set.
"I felt like she just put in all the balls that went out in the first set. I wanted to focus on myself no matter what was going on on the other side of the net and I kept going because the momentum can change for sure."
Swiatek next faces Australian qualifier Maddison Inglis, who progressed to the fourth round after her third-round opponent Naomi Osaka, twice Australian Open champion, pulled out of the Grand Slam due to an abdominal injury.
"Hopefully Naomi is well. I didn't know. I mean, she was playing great. I haven't watched, but I saw from the scores," Swiatek said. "She likes playing here as well. So I hope she's well.
"Yeah, it's exciting to be in the fourth round again. And guys, hopefully you're not going to be so harsh on me if I play an Australian.
"But there are a lot of Polish flags here. So yeah, please make it even."