Russia's Medvedev rolled through 6-4, 6-4, 6-2 in 1hr 55min, while Greek fourth seed Tsitsipas gained a 6-3, 7-5, 6-7 (2/7), 6-4 win over unseeded Frenchman Benoit Paire.
World number two and title favourite Daniil Medvedev has won over the Australian Open crowd as he eased into the last 16 along with Stefanos Tsitsipas.
Russia's Medvedev, the de facto men's top seed after the deportation of defending champion Novak Djokovic on the eve of the Grand Slam, on Saturday needed four sets and a large dose of composure to see off Australian showman Nick Kyrgios and silence Rod Laver Arena, but it was altogether more comfortable as he dismissed unseeded Dutchman Botic van de Zandschulp.
The 25-year-old Medvedev kept his cool in sweltering conditions on Margaret Court Arena to roll through 6-4, 6-4, 6-2 in 1hr 55min and faces American Maxime Cressy in the fourth round.
"I'll put it this way, it's easier to play a guy from the Netherlands than a guy from Australia in Australia in Melbourne," said Medvedev, who has a similar love-hate dynamic with the crowd in New York.
Greek fourth seed Tsitsipas, who is chasing a maiden major, was also largely untroubled in a 6-3, 7-5, 6-7 (2/7), 6-4 win over unseeded Frenchman Benoit Paire and plays American Taylor Fritz next.
Medvedev and Tsitsipas, two of the generation coming up fast behind the "Big Three" of Djokovic, Rafael Nadal and Roger Federer, could meet in the semi-finals.
Halep fires warning
After the drama of Friday, when defending champion Naomi Osaka exited Melbourne in the third round, the women's seeds were also mostly untroubled on day six.
In the women's draw, Halep swatted aside Danka Kovinic, conqueror of US Open champion Emma Raducanu - 6-2, 6-1 in just 64 minutes to set up a date with Cornet of France.
The fit-again Halep came into the tournament full of confidence after her first title in 16 months earlier this month at a Melbourne warm-up event and was always in charge.
"I feel great that I can play the fourth round again. I always love to play in Australia so that's why maybe I play good matches," said Halep, seeded 14.
World number two Sabalenka overcame the serving problems that have been plaguing her early season, but still needed three sets to get past 31st seed Marketa Vondrousova.
The Belarusian had served 70 double faults in her previous four matches in 2022, but only tallied 10 as she beat the Czech 4-6, 6-3, 6-1.
She now meets unseeded Estonian veteran Kaia Kanepi.