Eighth seed Musetti won 6-2, 4-6, 7-5, 6-2 against the 15th seed after over two hours 45 minutes on a windy Court Philippe Chatrier.

The 23-year-old next plays second seed Alcaraz, who blasted past American Tommy Paul 6-0, 6-1, 6-4, for a place in the final.

Alcaraz leads Musetti 5-1 in previous meetings including winning twice on clay this season -- in the semi-finals in Rome and the final in Monte Carlo.

"Honestly, I found really disrespectful for Tommy, for the ones who they play to have a question already about the semi-finals," said Musetti, when asked about meeting Alcaraz before the Spaniard's match had been played.

"There's a match to play, and honestly, I don't want to answer on this question."

For both Musetti and world number 16 Tiafoe -- twice a US Open semi-finalist -- it was a first last-eight appearance at Roland Garros.

And both struggled to find their feet.

"It was pretty windy and not that easy to find the right feelings with the ball, but I managed to win this incredible third set, which was probably the key of the match," said the Italian.

Musetti's serve proved to be a major weapon on the day as he fired down eight aces with an 81 percent success rate on his first serve in gusty conditions in Paris.

He also saved two of the three break points engineered by Tiafoe, who had 51 unforced errors to the Italian's 32.

The Italian is now 13-4 at Roland Garros, where he will contest his second Grand Slam semi-final following his run to the same stage at Wimbledon last year.

"A lot of junk shots today," said Tiafoe of his own performance.

"Yeah, he was just tougher in the winning-ugly department, because it wasn't going to be clean from either of us. It was really, really windy and tough conditions."