The Swiss had criticised organisers for doubling ticket prices after he confirmed his participation last weekend but the fans who had made their way into Foro Italico on Thursday have been rewarded with a Federer double bill.
With rain having washed out Wednesday’s play, Federer along with champion Rafael Nadal and top seed Novak Djokovic all faced back-to-back matches on Thursday if they want to reach the quarter-finals.
The backlog means that fans on the secondary Grandstand Court can also look forward to a blockbuster schedule as Federer will be back for an evening showdown with Croatian Borna Coric.
Earlier in the day, Nadal had treated the Grandstand fans to a 6-0 6-1 demolition of Frenchman Jeremy Chardy and the Spaniard will be back on action on the main stage against Georgia’s Nikoloz Basilashvili.
Djokovic, fresh from winning last week’s Madrid Open, registered a straight sets win over Canadian Denis Shapovalov.
Djokovic, 31, a four-time Italian Open winner, next plays either German Philipp Kohlschreiber or Italy’s Marco Cecchinato for a place in the quarter-finals.
The 37-year old Federer moved around the court like his younger self as he rifled in 17 winners in the opening set, having broken Sousa in the seventh game before he saved a triple break point, the last one with a stunning crosscourt forehand.
Having broken Sousa’s serve in the opening game of the second set, the Swiss maestro was at his best again in the seventh as he saved a double break point and went on to wrap up the entertaining contest.
“I came out of the blocks well and held serve throughout, so I am very happy to be in the next round,” said Federer.
“I played today already and Borna didn’t. I don’t know whether it’s a disadvantage or not but either way it’s going to be tough.”
After crashing out in the semi-finals on home soil in Madrid, Nadal wasted no time in making a statement of intent as he blew away Chardy.
Nadal won 80 percent of the points on both his first and second serve as he tormented the Frenchman with a barrage of stinging baseline shots.
In other matches, Fernando Verdasco ground out a surprise 4-6 6-4 7-5 win over fifth seed Dominic Thiem, as did Jan-Lennard Struff with a 6-2 6-3 hammering of Marin Cilic.