That left only Maria Sharapova and Angelique Kerber - who will meet in the next round - and French Open champion Jelena Ostapenko as Grand Slam winners in the women's draw.
Ninth-seeded Johanna Konta also struggled in a straight-set loss to lucky loser Bernarda Pera, an American who is ranked 123rd and making her Grand Slam debut.
Alarm bells were ringing for Kerber when Sharapova rifled away a backhand victor to earn a break point at 3-3 but the Russian missed a regulation forehand to waste the chance.
She broke back from 0-2 down in the second set and had a break point to get ahead, but otherwise the door was slammed shut by a very impressive and aggressive performance from the German.
Muguruza the current Wimbledon champion was put away by Su-Wei Hsieh from Taipei in what was a battle, but only for Muguruza to try and stay in the match.
The Rod Laver Arena evening clash between the only two grand slam winners left in the women's draw had the feel of a showpiece final rather than a third-round match-up but only 21st seed Kerber rose to the occasion.
Roger Federer and Novak Djokovic were nearly as ruthless in their straight-sets wins Saturday night, which is hardly surprising for two players with a combined 31 Grand Slam titles.
Sevastova's tricky game wore Sharapova down at Flushing Meadows and the 2008 champion appeared determined not to let that happen again, blasting her way to the first set in just 23 minutes.
"I came out and I was trying to enjoy every point".
'In the first set, I didn't return well.
"But I am very pleased where my game is at".
"I knew she was going to give me a lot of pressure", said Hsieh, who was ranked number one in doubles for five weeks in 2014. "It's never easy to play against top 20 girls", she said. After an hour and 38-minutes of play, Hsieh finally completed the huge upset - her second in a row - and sealed her spot in the second week.
Sharapova said Kerber was the more aggressive on court and took more risks.
After being broken once in the second, he then didn't face another break point for the rest of the match.
Djokovic looked far from his best but was still too good for the enigmatic world No39, maintaining his flawless record against Monfils with a 4-6 6-3 6-1 6-3 victory. There are few more demanding places to play than Melbourne Park on a hot January afternoon around 3pm, when the temperature hits a peak - at the end of last week it edged above 40°C. It was her 11th win, including the Sydney International title last week.
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