Wednesday at the Foro Italico was a complete washout after persistent rain in Rome.
It meant several players faced back-to-back matches to help get the schedule back on track.
Federer was the first of the trio to play and on Campo Centrale he saved seven break points in his first match at the Italian Open since May 2016.
The Swiss star broke Joao Sousa three times and hit 25 winners to win 6-4 6-3 in 80 minutes.
The 37-year-old will next play Borna Coric on Grandstand later this evening.
“I’m happy we got to play a good match. I think it’s a slippery court here, I must say,” he said.
“It’s tough to play I think for all the players. Every clay court plays slightly different: Monaco, Madrid, Barcelona, here, Paris. I think when it’s a bit nicer weather here, it slides a lot.
“I came out of the blocks well, had a good feeling. Didn’t get broken. That on clay in a first round is a good sign.”
On Grandstand, Nadal was in ruthless mood as he dismissed Jeremy Chardy in just 67 minutes.
He won 80 per cent of the points on both his first and second serve as he bullied Chardy with a barrage of heavy baseline shots.
And the reigning Italian Open champion was pleased with how he played to set up a third-round match against Georgia’s Nikoloz Basilashvili on Centrale.
“It was a good start today,” Nadal said.
“[I’m] happy with that victory and happy because it was one hour, and that’s important for what’s coming up. Nikoloz is a tough player, very dangerous. He hits the ball very strong.
“He already won two great matches here so it’s going to be a big challenge, but it’s a good test for me.”
And world No 1 Djokovic needed one less minute than Nadal to beat Denis Shapovalov 6-1 6-3.
The Serbian showed little mercy to the young Candanian as he made just 11 unforced errors and won 88 per cent of points on his first serve.