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Swiatek was irrepressible against the 18-year-old American, extending her head-to-head dominance to 4-0 with a 6-0 6-3 victory in 66 minutes.
The Pole won the first eight games of the match and always appeared in control with her reliable forehand a key feature.
Swiatek laced 13 winners with only nine unforced errors, breaking Gauff five times. The American committed 26 unforced errors for the match.
The victory is Swiatek's 62nd of the season, moving her closer to Angelique Kerber's 2016 mark of 63.
Swiatek will face No.4 seed Jessica Pegula in the semi-finals as the Pole aims for her eighth WTA title of the season.
Pegula secured her berth in the final four with a 6-4 7-5 victory over compatriot Madison Keys in their first meeting in one hour and 34 minutes.
No.3 seed Aryna Sabalenka was a surprise casualty as Croatian qualifier Donna Vekic continued her excellent week with a 6-4 6-7 (5-7) 6-1 in two hours and 37 minutes.
World No.77 Vekic has beaten former world No.3 Maria Sakkari and two-time Major finalist Karolina Pliskova this week.
No.2 seed Paula Badosa was also bundled out by American Danielle Collins 7-6 (7-5) 6-4. Collins will meet Vekic in the last four.
