Defending champion Sabalenka had not dropped a set before facing the Czech sixth seed, who fired 18 aces and saved seven of nine break points but faltered when leading by a break in the final set.
"What a battle. What an incredible player she is. I'm speechless right now because I was pushing myself to the limit this match," said Sabalenka.
The Belarusian broke in the second game, whipping a forehand into the corner that Noskova did not even attempt to chase down, but the Czech broke back with a pair of powerful groundstrokes from the baseline in the ninth.
Sabalenka, who reached a record 21 consecutive tiebreak wins at the slams earlier this year, was completely in her element in the opening-set tiebreak, where she sprinted through the first six points.
But her firepower deserted her in the second set and she struggled to contain Noskova's serve before handing the Czech a 4-2 lead with a double fault.
After levelling the contest at one set all, Noskova set about pressing home her advantage.
Sabalenka screamed in frustration when a pair of double faults midway through the third set helped her opponent secure another break. Noskova seemed to be heading for an upset win before Sabalenka recovered her poise to level the contest in the eighth game.
And the Belarusian was right at home again in the decisive tiebreak, clinching it with an ace before giving credit to the fans for helping to propel her to the win.
"I honestly thought, 'this is it'," said Sabalenka. "It's a tough match, tough battle."
