Alcaraz beats Davidovich Fokina to keep Barcelona defence on track
Alcaraz's build-up to the French Open next month has been slowed by hand and back problems which forced him to pull out of Monte Carlo, and the top seed was made to work hard by Davidovich Fokina.
The teenager broke in the first game of the match but Davidovich Fokina hit back for 3-all before Alcaraz soon regained the upper hand.
However, he failed to close out the first set when serving at 5-4 and Davidovich Fokina fought his way to within two points of taking the opener in the tie-break.
Alcaraz though held his nerve as the 38th-ranked Spaniard faltered, with Davidovich Fokina belting a forehand long to eventually surrender the set.
The US Open champion saved six break points in the third game of the second set and then broke immediately after for a 3-1 advantage.
Davidovich Fokina again responded to get back on serve, and it stayed that way until Alcaraz broke in the final game to seal victory.
He will take on the winner of the quarter-final between Argentina's Francisco Cerundolo and Briton Dan Evans.
Stefanos Tsitsipas eased into the semi-finals earlier in the day, beating Alex de Minaur 6-4, 6-2.
Tsitsipas claimed the lone break of the opening set and then reeled off five straight games in the second as he won for the ninth time in as many meetings with Australia's De Minaur.
The Greek second seed will play Lorenzo Musetti on Saturday as he bids to reach the Barcelona final for a third time. He was runner-up to Rafael Nadal in 2018 and 2021.
Tsitsipas, the losing finalist at January's Australian Open, is bidding for his first title of the season. He lost to Alcaraz in the quarter-finals in Barcelona last year.
Musetti advanced via walkover when fellow Italian Jannik Sinner had to pull out because of illness.
"Sad to have to withdraw from my match today in Barcelona," tweeted Sinner, who beat Musetti in the Monte Carlo quarter-finals last week.
"I've been feeling unwell for a few days now. Today the sickness got worse and I'm not able to play. I'll take some time to rest and recover."