Swiatek, 22, of Poland, started a little slowly and dropped serve early having broken her opponent, but moved through the gears in what was her first match on Centre Court.
Once she found her range with her lethal forehand, the four-time Grand Slam champion was unstoppable as she cruised to a Tour-leading 40th win of the season.
World number one Swiatek, a clay court specialist with three French Open titles to her name, has found Wimbledon’s grass tricky in the past with her longest run coming in 2021 when she reached the fourth round.
She has started her fourth appearance in ominous fashion, however, dropping only six games in her opening two matches.
“I’m happy that I can play such a solid game and kind of do what I was practicing,” Swiatek said on court.
“I feel pretty confident and pretty happy. Which doesn’t happen often, honestly. So I’m happy that this is the first year where I finally kind of feel like I learned a lot and I can really adjust my game to grass courts a little.”
Swiatek broke Sorribes Tormo’s serve for a 2-0 lead but was broken back in the following game before really stamping her authority on the contest as the sun made an appearance.
Her Spanish opponent played her part in entertaining rallies in the opening set, but Swiatek always had an extra weapon in her armory.
The second set was all over in a flash, meaning the Centre Court crowd were treated to a little over two hours of tennis in the first two scheduled matches of the day.
Kostyuk and Sakkari endured three rain interruptions before Kostyuk prevailed 0-6, 7-5, 6-2.
She became only the third women’s player to beat a top-10 seed at Wimbledon in the Open era after losing the first set 6-0.
Reuters contributed to this report.
Top seed Iga Swiatek headlines women’s Day 3 Wimbledon matches