It kept the 23-year-old Pole on course in her bid to become the first woman this century to win the same WTA 1000 title four times in a row.
But Swiatek, the world number two, had to work hard after dropping a set at the tournament for the first time since 2022 in Wednesday's last-16 clash.
Czech Noskova, ranked 33, fired down nine aces - a tournament high for a single set - as the opener went to a tiebreak, which the underdog won convincingly.
Swiatek, without a title win since her fourth French Open success last June, finally cracked the Noskova serve in the second set on her way to levelling the match.
The second seed then clinched a tight decider with a break for 5-4 and wrapped up a 6-7 (1-7) 6-4 6-4 win in two hours and 32 minutes.
"Every match against Linda is always super tough," said Swiatek in her on-court interview.
"This was another won and I'm proud I was solid until the end but it wasn't easy with her serve, which was kind of perfect."
Swiatek will take on fifth seed Elena Rybakina in the last eight in a rematch of last year's final.
"Elena is a really experienced player and you have to be 100 per cent to win," she added. "So for sure I will use my experience, but it's going to be a tough battle."
Swiatek and Rybakina are the highest seeds left in the draw after Jelena Ostapenko beat fourth seed Jasmine Paolini 6-2 6-2.
Rybakina earlier said she was "disappointed" that her long-time coach Stefano Vukov remains banned by the WTA following the conclusion of an investigation.
The governing body revealed last month the Croatian was provisionally suspended from holding an official role at tournaments after Rybakina announced he was rejoining her team.
Concerns have been raised over several years regarding Vukov's behaviour towards Rybakina, who he coached to the Wimbledon title in 2022.
Speaking to reporters after her win over Rebecca Sramkova in Doha, Rybakina said: "I'm just disappointed with the situation, and how the process went. I'm not going to comment much on that any more."
Rybakina, who had split from Vukov ahead of the US Open last summer before rehiring him, made it clear in Australia last month that she did not support the suspension.
"I don't agree with a lot of things what WTA do in the sense of my relationship with Stefano," she said at the time.
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