The third seed was on court for just 34 minutes on Thursday as last-16 opponent Anna Kalinskaya was forced to retire through injury at 6-2 1-0 down.
Sakkari has enjoyed a successful year on the WTA circuit, reaching grand slam semi-finals for the first time in her career at the French Open and US Open.
Through to the quarter-finals in the Russian capital, where she will play Simona Halep, the 26-year-old becomes the first Greek woman to qualify for the year-end WTA Finals in Mexico.
Eighth seed Halep beat Veronika Kudermetova 6-1 7-6 (7-4), while world number 35 Marketa Vondrousova also prevailed in straight sets against Ukrainian Lesia Tsurenko.
Elsewhere, Ostrava Open champion Anett Kontaveit is through to her eighth quarter-final of 2021 after defeating Andrea Petkovic 6-1 6-4.
Meanwhile, at the Tenerife Open, fourth seed Camila Giorgi enjoyed a commanding 6-1 6-2 victory over Montenegro's Danka Kovinic.
However, there was no joy for seventh seed Clara Tauson as the Danish teenager went down 7-6 (7-4) 2-6 6-4 against China's Saisai Zheng.