World number one Novak Djokovic had to save two match points against Juan Martin del Potro before advancing to the Italian Open semi-finals.
The Serb, 31, will play Argentina's Diego Schwartzman on Saturday after beating his compatriot Del Potro 4-6 7-6 (8-6) 6-4 in Rome.
Earlier, defending champion and eight-time winner Rafael Nadal beat fellow Spaniard Fernando Verdasco 6-4 6-0.
Nadal came from 2-0 down to reach the semi-finals in one hour 38 minutes.
The 32-year-old, who has lost in the semi-finals of his past four tournaments, next faces 20-year-old Greek Stefanos Tsitsipas, who went through following the withdrawal of Roger Federer.
World number three Federer, a four-time finalist in the Italian capital, was unable to compete because of a right leg injury.
The Swiss, 37, was playing the Italian Open for the first time since 2016 and saved two match points to defeat Borna Coric 2-6 6-4 7-6 (9-7) on Thursday, having beaten Joao Sousa in straight sets earlier in the day.
"I am disappointed that I will not be able to compete today," said the 20-time Grand Slam champion.
"I am not 100% physically and after consultation with my team, it was determined that I not play.
"Rome has always been one of my favourite cities to visit and I hope to be back next year."
Djokovic and Nadal through
Del Potro won the opening set against Djokovic in 62 minutes after some pulsating groundstrokes - only the second set he had taken against Djokovic on clay in their fourth encounter.
Djokovic lost a 5-2 lead as the second set went to a tie-break, but then played an audacious backhand drop shot from the back of the court when facing a second match point and duly took the contest to a decider.
The four-time winner in Rome then sealed the win with an ace on his first match point.
"I had luck in the decisive moments in the second set tiebreak," Djokovic said.
"He was playing really well. Gave me a lot of trouble. But I never lost faith. I'm just really pleased to overcome."
World number 24 Schwartzman, Djokovic's last-four opponent, secured his place in the semi-finals with victory over Japan's Kei Nishikori.
Nadal, a 17-time Grand Slam winner, conceded only two games in his matches against Jeremy Chardy and Nikoloz Basilashvili on Thursday, but had to save a point to prevent a 3-0 deficit against fellow left-hander Verdasco.
He survived three break points at 4-4 in the first set but needed only 36 minutes to win the second.