World number one Swiatek broke Collins seven times, faced only two break points and wrapped up a one-sided match in a tidy 59 minutes.
"I feel like I was really solid and I didn't make a lot of unforced errors," Swiatek said in her on-court interview.
"I really like playing that way because it gives me confidence and I can be proactive from the beginning to the end so I am pretty proud of today."
Swiatek raced out to 3-0 lead in the opener and, after both players swapped service breaks, the top-seeded Pole held to love before closing out the set with her fourth break.
It was more one-way traffic in the second set as a fully focused Swiatek shifted into cruise control and barely broke a sweat in a match she ended in style with a break to love.
Earlier, Jessica Pegula had her hands full in her first match since winning last week's Canadian Open as the American overcame a slow start to secure a gutsy 6-7(2), 6-2, 6-3 win over Italian qualifier Martina Trevisan.
Pegula comfortably lost the first-set tiebreak but showed her quality in the second set before racing out to a 3-0 lead in the decider en route to her 27th hardcourt win this year.
In the evening, second seed Aryna Sabalenka fended off a third-set comeback attempt by qualifier Ann Li of the U.S. to notch a 7-5, 2-6, 6-4 victory and set up a meeting with Russia's Daria Kasatkina.
After trading the first two sets, the Belarusian appeared in control when she jumped out to a 5-1 lead in the decider but her 192nd-ranked opponent had other ideas, winning three straight games to whittle the lead down to a single game.
Despite the rising pressure the hard-hitting Sabalenka kept her cool, sealing the win with an unreturnable serve on match point to improve to 42-9 on the year.
Fourth seed Elena Rybakina also came through a three-set slugfest to defeat Jelena Ostapenko 6-7(6), 6-2, 6-4 to reach the round of 16.
Rybakina crushed 11 aces to raise her season-leading tally to 392 and will next face Italy's Jasmine Paolini for a place in the quarters.
Veteran American Venus Williams started strong against Zheng Qinwen before succumbing to a 1-6, 6-2, 6-1 defeat at the hands of the Chinese player.
Williams received a wild card into the U.S. Open earlier on Wednesday and will be competing at the year's final major in New York for a record-extending 24th time.
In other action, American teenager Coco Gauff, seeded seventh, breezed past Egyptian Mayar Sherif 6-2, 6-2, Wimbledon champion Marketa Vondrousova beat Anastasia Potapova 6-4 6-2 and Kasatkina overcame lucky loser Varvara Gracheva 6-3 6-1.
