While the top seed did not have it all her own way in the second set, she ultimately had more than enough to see off Fett 6-0 6-3.
All early signs pointed to a comfortable win for Swiatek as world number 252 Fett looked nervous, committing 14 unforced errors to her opponent's four in the first set.
As such, Swiatek's first-set bagel arrived with the Pole barely breaking a sweat, but her level dropped in the second and allowed Fett a foothold.
Fett broke to love in the first game of the second set, and although Swiatek instantly hit back, the Croatian then broke again before managing to consolidate and go 3-1 up.
But she passed up five break points as Swiatek began to build her way back, and the world number one was soon a break to the good, with Fett's 23 unforced errors, which included nine double faults, proving her downfall.
A sloppy return from Fett gave Swiatek match point, and the former put her next shot straight into the net as the favourite became the first female player since Martina Hingis in 1997 to win 36 successive matches.