The fourth-seeded Rublev eased past American Marcos Giron, 7-6 (1), 6-3, after 79 minutes. The 23-year-old saved four of the five break points he faced in winning his ninth match in 10 played this season.
Rublev, coming off leading Russia to the ATP Cup title with Daniil Medvedev before losing to his countryman in the Australian Open quarterfinals, thrived at the 500-level in 2020, picking up three consecutive titles after the ATP Tour restarted at Hamburg, St. Petersburg and Vienna. He and Murray have faced off just once before, with Murray taking their second-round encounter four years ago at Melbourne Park.
"Andy is a true legend and I have a really good connection with him. I really like him as a person and as a player," Rublev told the ATP website. "He destroyed me once in the past. I’m sure we’ll have great, long rallies and it will be a fight."
Fellow Russian Karen Khachanov also advanced, upstaging 2015 champion Stan Wawrinka, 6-4, 7-5. One break in each set was all Khachanov required in leveling his head-to-head series with the Swiss to 2-2. The 24-year-old, who won 10 of his 11 net points, gets Cameron Norrie in the second round.
Second seed Stefanos Tsitsipas launched his tournament with a 7-6 (4), 7-5 victory against Egor Gerasimov. Tsitsipas let break advantages slip in both sets, but fended off last week's Montpellier semifinalist by compiling 31 winners (15 forehand) to 29 unforced errors. The Greek will next battle Hubert Hurkacz, a 6-3, 7-6 (6) winner over Adrian Mannarino.
Alex de Minaur emerged victorious in an all-Australian battle by dismissing John Millman, 6-1, 6-4. De Minaur won an impressive 52 percent of his first-serve return points to break his compatriot six times from eight chances. The Sydney native will meet Kei Nishikori, who eliminated No. 7 seed Felix Auger-Aliassime Monday, for a place in the quarterfinals.
In a clash of Frenchmen, Jeremy Chardy squeaked past Ugo Humbert, 4-6, 7-6 (5), 7-6 (4), by erasing a 2-5 deficit in their deciding set. Chardy awaits Montpellier champion David Goffin or Jan-Lennard Struff, a first-round match taking place Wednesday.