Sousa needed to save four match points to beat his American opponent 6-3 6-7 7-6 in the first round.
He will now face Federer on Wednesday afternoon, in their second meeting.
In 2014, Federer beat Sousa in three sets at the Gerry Weber Open in the three round.
But Federer will be facing an even more determined Sousa when they take to court at the Foro Italico tomorrow.
Last month, Sousa was asked who he would like to beat before he quits tennis and the 30-year-old name-checked Federer as the man that is top of his list.
He told Punto de Break: “If I could choose someone, I would like to beat Federer.
“I only played once with him, in Halle, he beat me in the third set.
“He is a player that is a world-renowned, considered one of the best in history.
“It is not a goal, but I hope I can beat him before he retires.”
Federer has opted to play in Rome at late notice and it is his first appearance at the event since 2016.
But the Swiss star is excited to get more clay court matches in his legs.
“I’ve just come from practising for five weeks after Miami,” he said.
“I think I was playing well in Madrid, so I just said, again, ‘Let’s come to Rome,’ a city I like so much as well.
“There would be excitement, more excitement than me coming to a practice court in Switzerland. I thought that would be nice.
“Honestly, I love to play matches. Regardless of what happens here, I just think it’s good for me to play matches at this stage.
“I’m very happy to be here. I’m pumped up to play well. I mean, my excitement couldn’t be bigger.”