Former US Open winner Medvedev fought through in just shy of three hours on Court Rainier III against Khachanov, after having been a set and a break up on his fellow Russian.
After an early exit from the Miami Open last month caused the 29-year-old to exit the top 10, Medvedev got back to winning ways on clay as he chases his first title since claiming the Rome Open two years ago.
Elsewhere, 11th seed Ben Shelton was stunned by 42nd-ranked Alejandro Davidovich Fokina and there will be no showdown between Novak Djokovic and Stan Wawrinka after the Swiss was defeated by Alejandro Tabilo.
Shelton went down 6-7 (2/7), 6-2, 6-1 to his Spanish opponent, who reached the 2022 final at Monte Carlo.
Wild card Wawrinka also played out an epic that lasted nearly two-and-a-half hours before succumbing 1-6, 7-5, 7-5 to Chile’s Tabilo.
France’s Gael Monfils beat Hungarian Fabian Marozsan 4-6, 6-1, 6-1 and Matteo Berrettini set up a second-round meeting with top seed Alexander Zverev after winning in straight sets against Mariano Navone.
Felix Auger-Aliassime went down to German qualifier Daniel Altmaier 7-6 (7/5), 6-3, but fellow top 20 player Lorenzo Musetti avoided a similar fate by coming back from a set down to defeat qualifier Bu Yunchaokete of China.
Jiri Lehecka of the Czech Republic beat American Sebastian Korda and Marcos Giron overcame fellow North American Denis Shapovalov, both in straight sets. (AFP)
