The 19-year-old Spanish phenom battled back after losing the first set, going on to win 6-7 (5-7), 6-2, 6-4.
“It’s a challenge facing a player like Fabio. He’s a great player with a lot of talent,” Alcaraz said after the dramatic clay-court duel.
“You never know what he might have in store for you.”
Fognini, a 35-year-old veteran with nine singles titles, went down 3-0 to the defending champion in the opening set, before battling back with a string of masterful rallies.
He broke Alcaraz’s serve to equalize at 5-5, then won the set in a tie-breaker.
But Alcaraz roared back in the second, going up 4-0, and carried his momentum through the final set to take the match.
The dramatic display had the crowd at the stadium court fired up.
“You energized both Fabio and me from the start, thank you so much,” Alcaraz told the fans.
“We played a great match. I’m very happy I managed to win.”
Alcaraz will face the winner of an all-Serbian showdown in the quarter-finals Friday: either 57th-ranked Laslo Djere or 80th-ranked Dusan Lajovic.
Alcaraz, who returned last week from a four-month injury break, is looking to rekindle the magic he unleashed last year in Brazil.
Then, he won the Rio Open on his way to racking up five titles, including the US Open, and becoming the youngest-ever world number one in the ATP rankings — a spot he has now lost to Novak Djokovic after struggling with injuries.
Alcaraz opened his title defence in Rio by winning a tougher-than-expected, rain-delayed match against 556th-ranked Mateus Alves of Brazil Wednesday.
He made his 2023 debut last week by winning his seventh career ATP title at the Argentina Open.
AFP