Two Russians have already booked their place in the last 16 at the All England Club.
The result made it two Russian men already in the last 16 at the All England Club with the chance of a third if Daniil Medvedev can triumph over Marin Cilic on Saturday.
Rublev had not made it past round two in any of his previous appearances at the Championships but a 6-3 5-7 6-4 6-2 victory extended the 23-year-old’s best-ever run at SW19.
Karen Khachanov was the other Russian to progress from round three on Friday, and in fine fashion with a 6-3 6-4 6-4 success over Frances Tiafoe.
Maryland-born Tiafoe had made headlines with a first-round win over Stefanos Tsitsipas but he had little answer to the big-serving 25th seed.
Khachanov sent down 13 aces and offered up no break points to progress into the second week like he achieved back in 2018.
Roberto Bautista Agut showed his pedigree on grass with a hard-fought 7-5 6-1 7-6 (4) victory against Dominik Koepfer.
A surprise semi-finalist at the 2019 tournament, the Spaniard made it into week two for a fourth time from six appearances in the main draw.
Bautista Agut only registered 18 unforced errors and the 33-year-old will face the winner of the Friday night Centre Court battle between Andy Murray and 10th seed Denis Shapovalov.
Chilean Cristian Garin was the other player to book his place in the last 16 during the afternoon.
A 6-4 6-3 4-6 6-4 triumph over Pedro Martinez saw the 25-year-old extend his best-ever run at the All England Club.
Before this year’s competition, Garin had never won a match at Wimbledon but could now be set for a date on the main stage next week with defending champion Djokovic if the Serbian can get the better of American Denis Kudla.