Carlos Alcaraz defeated Australia's world number 69 Aleksandar Vukic 7-6 (7/5), 6-2, 6-2 on the back of 42 winners.
Novak Djokovic held off a late rally from his American opponent on Court Philippe Chatrier to clinch a 6-3, 6-2, 7-6 (7/1) victory
Rafael Nadal overcame a freak injury scare when he accidentally hit himself with his own racquet to reach the US Open third round on Thursday.
Australian Open: Fabio Fognini had an angry ending to his match against Salvatore Caruso, and will face Alex De Minaur in his next fixture.
World number 16 Fabio Fognini has been forced out of the ATP Sardegna Open after testing positive for COVID-19.
Novak Djokovic believes the tennis season will restart with a series of regional tournaments because of the complexities of easing coronavirus restrictions worldwide that would allow players to travel.
Norway's Casper Ruud, a product of Rafael Nadal's tennis academy in Mallorca, has beaten top-20 players John Isner and Fabio Fognini.
Rafael Nadal, who won his fourth title in Canada a year ago, needed almost two hours on Friday to overcome the Italian veteran who shocked him on clay at Monte Carlo in April.
Fabio Fognini was beaten by US world number 94 Tennys Sandgren 6-3, 7-6 (12/10), 6-3 on the compact Court 14.
Novak Djokovic, winner of the last three Grand Slam tournaments, is now over 3,000 points clear of rival Rafael Nadal.