Serve figures from the contest were uneven: eight aces and eight double faults, with only six of 24 points won behind a second serve.
The 21-year-old world number eight played with controlled aggression and served brilliantly.
She stayed composed throughout and broke Gauff's serve four times in the first set alone.
Noskova fittingly sealed the victory with an ace, taking a place in the last four at the first time of asking.
Fourth-ranked Gauff can still qualify for the semi-finals. Pegula can as well.
In another match, Pegula made only five unforced errors to Kostyuk's 17 as she took the first set.
The home favourite quickly went up a break in the second set.
Four breaks of serve then ensued. Pegula sealed the decisive break at 5-5 before serving out the victory.
Sabalenka won her WTA Finals opener despite a wayward serve.
Noskova's straight-sets win over Gauff was the clearest result of the day, built on early breaks and a closing ace.