Fearnley prevailed 6-2 6-3 but had to turn around the run of play in each set against a determined opponent.
Italian Fognini, 37, had revealed he was playing in this tournament in Rome for the final time.
“I think it’s a good time to say goodbye in this beautiful city, special city,” Fognini, who first appeared at the Italian Open in 2006, told the Tennis Channel.
“Since I was a kid I was coming here,” he continued. “And now I’m in the opposite [end of my career].
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“But I’m here with a smile on my face because I know that I had a really difficult time during my, I don’t know, 20 years in Rome and I would like to enjoy the last lap.”
Fognini has won eight of his nine ATP singles titles on clay, including the 2019 Monte Carlo Masters.
Ultimately Fearnley proved too strong for him as he set up a clash with another home favourite and 2021 Wimbledon finalist Matteo Berrettini in the next round.
Fearnley has risen to 57 in the ATP world rankings after beating a top-20 player, Czech Republic’s Tomas Machac, for the first time at the Madrid Open last month.
The 23-year-old, who lost to Grigor Dimitrov in the second round in Madrid, recovered after losing his opening service game against Fognini to break serve three times on his way to taking the first set in 34 minutes.
Fognini also started the second set strongly, breaking Fearnley’s serve again in the opening game of the set to lead 3-1.
But the Briton came storming back to reel off five games in a row, sealing his victory on his first match point in one hour and 21 minutes.
Fearnley acknowledged: “It was a tough match. I really had to dig deep in both sets.
“I knew I had to up my game in order to win. Very happy to get the win.
“I was telling myself just to stay composed,” he explained. “I kind of expected to get off to a slow start, so just happy to get through.”
There a unique moment during the match when the selection of the new Pope was announced live to the crowd in the stadium.
“The Italian fans were amazing,” Fearnley added. “It was an electric atmosphere and it was a really amazing atmosphere to play in.”
The four other British players in the tournament will be in action on Friday, with Emma Raducanu, Jack Draper, lucky loser Cameron Norrie and Sonay Kartal all playing, live on Sky Sports Tennis.