Daniil Medvedev saw his woe on clay continue as he was beaten by fellow Russian Aslan Karatsev, but Rafael Nadal is safely through.
The French Open hopes of Simona Halep appear to be in doubt after injury ended her clash with Angelique Kerber in Rome.
Both Serena Williams and Naomi Osaka lost in Rome, the former suffering defeat in her 1,000th career match.
World number one Novak Djokovic was broken twice in the second set, but Taylor Fritz could not take the top seed the distance in Rome.
Belinda Bencic was the highest seed to be eliminated on Tuesday, though Garbine Muguruza had no such issues.
After practicing with Novak Djokovic in Rome on Sunday, Andy Murray is a late addition to the doubles draw along with Liam Broady.
Taylor Fritz progressed to a meeting with world number one Novak Djokovic in Rome, while Rafael Nadal will face Jannik Sinner.
Magda Linette dominated the first set against Petra Kvitova in Rome, but the Czech responded emphatically to reach the second round.
Five-time Queen's Club Championships winner Andy Murray will compete for the 2021 title ahead of a possible Wimbledon return.
Despite falling behind to Matteo Berrettini, Alexander Zverev claimed his first Masters 1000 title since 2018 in Madrid on Sunday.