Both players struggled to find their rhythm throughout the match in the early hours of Monday Warsaw time, with a large number of unforced errors on both sides: 52 by the Polish world No. 1 and 55 by Nosková.
In the end, Świątek won the hard-fought two-hour and 33-minute court battle 6-7, 6-4, 6-4.
While the victory improved Świątek's tour-leading record to 22-2 this season, it also marked her first comeback win from a set down in 2024.
"As you can see, it's not like we can take everything for granted," Świątek said after the match.
"You can be in trouble at the early stages of the tournament, so there's no sense to talk about the Sunshine Double," the Polish star added, referring to her bid to become the second woman ever to win the Sunshine Double twice.
The Sunshine Double is when a player captures the Indian Wells and Miami Open titles in the same season.
Only Germany's Steffi Graf has achieved this feat so far - in 1994 and 1996, while Świątek got her first Sunshine Double in 2022, and already won the Indian Wells this year.
Now, in the Miami Open round of 16, Świątek will on Monday face Russia's 16th-ranked Ekaterina Alexandrova, who advanced to the last 32 with a 6-4, 3-6, 6-3 win over countrywoman Anastasia Pavlyuchenkova.
The Polish star leads the head-to-head against Alexandrova 3-1.
This year's Miami Open runs until March 31.
(mm/gs)
Source: PAP, IAR, WTA, Sport.pl, Weszlo.com