World No. 3 Federer was barely troubled as he dismissed Portugal's Joao Sousa 6-4, 6-3 in 1 hour, 21 minutes, while world No. 2 Nadal required little over an hour to sweep aside Frenchman Jeremy Chardy 6-0, 6-1. Djokovic also recorded a straight-sets victory as he dispatched Canada's Denis Shapovalov 6-1, 6-3.
Federer, returning to the Foro Italico for the first time since 2016, had criticised organisers for doubling ticket prices when he confirmed his participation last weekend, but those who have tickets will be treated to a double bill of all three top players after rain washed out play on Wednesday, forcing the trio into back-to-back matches.
Elsewhere, Nick Kyrgios was disqualified for throwing a chair on court just hours after launching a scathing attack on his fellow players on a podcast. Norway's Casper Ruud was awarded the match against the Australian when he led 6-3, 6-7 (5), 2-1.
Croatia's Marin Cilic also suffered an upset as he was defeated 6-2, 6-3 by German Jan-Lennard Struff. The 28-year-old faces No. 6 seed Kei Nishikori on Thursday evening, after the Japanese star beat Taylor Fritz comfortably earlier in the day, 6-2, 6-4.
No. 8 seed Stefanos Tsitsipas is also through after overcoming Italian qualifier Jannik Sinner 6-3, 6-2, while No. 7 seed Juan Martin del Potro advanced with ease, following a 6-4, 6-2 victory over Belgian David Goffin.
The British No. 1 lost a tightly contested first set -- which lasted more than an hour -- in a tiebreak, but recovered to level the match and then ease through the third and final set against the 2017 US Open champion.
Konta will face Venus Williams in the third round later on Thursday. The American was scheduled to face her sister, Serena Williams, in the second round, but the younger Williams sister withdrew from the tournament with a knee injury.
Meanwhile, world No. 1 Naomi Osaka beat Dominika Cibulkova in straight sets 6-3, 6-3 and No. 5 seed Petra Kvitova made short work of Yulia Putintseva, defeating the Kazakh player 6-0, 6-1. Next up for the two-time Wimbledon champion is Maria Sakkari, who dismissed No. 14 seed Anett Kontaveit 6-3, 6-2.
No. 3 seed Simona Halep unexpectedly exited the tournament with a 2-6, 7-5, 6-3 loss to Czech Marketa Vondrousova. Halep -- a former world No. 1 and the winner of last year's French Open --was runner up in Madrid last weekend.
Spain's Garbine Muguruza overcame Danielle Collins 6-4, 4-6, 6-2. Muguruza faces former world No. 1 Victoria Azarenka in the next round, while Osaka will compete against Mihaela Buzarnescu, who came through after Julia Goerges retired with the score 6-4, 3-6, 4-4.
Madrid Masters champion Kiki Bertens fended off a comeback by Amanda Anisimova, emerging with a 6-2, 4-6, 7-5 victory. Bertens faces Carla Suarez Navarro in the third round, after France's Alize Cornet retired against the Spaniard while trailing 6-0, 3-0.
No. 13 seed Madison Keys was eliminated by fellow American Sofia Kenin, who came from a set down to win 6-7 (2), 6-3, 6-4. The 20-year-old comes up against Karolina Pliskova in the third round, with the Czech having eased to a 6-3, 6-3 victory over Ajla Tomlijanovic on Tuesday.