The second seed has been in impeccable form and she thrashed unseeded Belgian Kirsten Flipkens 6-1, 6-0 to set up a meeting with 19th seed Ekaterina Makarova, who beat fifth seed Angelique Kerber 7-5, 6-4.
Sharapova, the 2008 champion, has only dropped five games in four matches so far in her bid for a second Australian title, the fewest games conceded to make the quarters in Melbourne in the Open era.
Monica Seles (1991 and 1993) and Steffi Graf (1989) previously held the record at eight games.
But Sharapova narrowly missed the all-Grand Slam mark held by Mary Pierce, who dropped only four games in making the last eight at the French Open in 1994.
“I’m certainly happy that I’m playing this well but it’s now the quarter-finals and it only gets tougher,” Sharapova said, adding that it was important to keep her concentration.
“It’s really about keeping your focus, no matter what the score is, no matter if you’re up,” Sharapova added.
The second seed, who needs to reach the final to have a chance of returning to World No 1, had beaten Flipkens in both of their previous matches.
She held serve and then, helped by some loose Flipkens shots, got the break for 2-1. Flipkens had two break point chances in the next game but failed to convert as Sharapova held.
The four-time Grand Slam winner was starting to get the measure of her opponent on a hot Melbourne day and raced to the set when Flipkens sent a forehand long.
It was more of the same in the second set as the Belgian lost confidence with the Russian racing through it in just 25 minutes.
Sharapova now plays Makarova in a repeat of their last-eight clash in 2012, when she won and went on to make the final, losing to World No 1 Victoria Azarenka.
Makarova is looking for revenge.
“I really want to play against Maria as I lost to her last year,” she said. “I’m confident and like my game so I think it will be really interesting. I think I’m more prepared this year. Last year I was surprised to get so far, but this time I’ll be ready,” she added.
Polish fourth seed Radwanska also powered into the last eight, winning her 13th match in a row without dropping a set by thumping Serbian Ana Ivanovic 6-2, 6-4. She now meets Li on Tuesday for a place in the semi-finals after the Chinese battled past Julia Goerges 7-6 (8/6),