All received byes into round two at the Foro Italico in Rome as top-eight seeds, and none dropped a set in booking last-16 places. 

Men's number one seed Djokovic, playing in his first tournament since being disqualified from the US Open for striking the ball into a line judge, beat Italian wild-card Salvatore Caruso 6-3, 6-2.

The Serbian will play compatriot Filip Krajinović in round three.

Reigning champion Nadal, who opted against competing at the US Open, faced a man who reached the semi-finals in New York - fellow Spaniard Pablo Carreño Busta.

Nadal broke his opponent five times en route to a 6-1, 6-1 thumping.

Italian fourth seed Matteo Berrettini was also victorious, defeating Argentina's Federico Coria 7-5, 6-1, and there is guaranteed to be an Italian in the quarter-finals as wild-card Stefano Travaglia is Berrettini's next opponent.

The day's biggest upset also came at the hands of an Italian, as 19-year-old Jannik Sinner - another wild card - toppled number three seed Stefanos Tsitsipas of Greece 6-1, 6-7 (9-11), 6-2.

Belgium's sixth seed David Goffin also fell, losing 6-2, 6-2 to Croatia's Marin Čilić.

In the women's singles, Italian Jasmine Paolini broke Halep five times but still could not beat the top seed.

With her serve wobbling, Romania's Halep broke Paolini on eight occasions and triumphed 6-3, 6-4.

Czech number two seed Plíšková beat compatriot Barbora Strýcová 6-3, 6-3, while fourth seed Elina Svitolina of Ukraine beat Russia's Anastasia Pavlyuchenkova 6-3, 7-6 (7-4).

Neither Svitolina or Halep travelled to New York.

In first-round action, Belarus' US Open runner-up Victoria Azarenka recorded a 7-6 (9-7), 6-2 win over Venus Williams and will face another American - number three seed Sofia Kenin - next.

Switzerland's Belinda Bencic was the top-ranked women's player to exit the Italian Open today, losing 6-3, 6-1 to Montenegro's Danka Kovinić.

The tournament, being played behind closed doors, is due to reach its climax on September 21 and continues tomorrow.