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Paul produced a spirited display and the momentum was with him when he impressively took the opener, only for Alcaraz to fight back for a 5-7 6-4 6-2 6-2 victory on No.1 Court.

At 21 years and 65 days old, the victory made Alcaraz – who beat Novak Djokovic in an epic final last year – the youngest player to reach the last four of the Wimbledon men's draw in successive editions since fellow Spaniard Rafael Nadal in 2006 and 2007 (21 years, 33 days).

He was made to work for the win, though, with Paul taking a 73-minute opener that showcased some terrific rallies, hitting a wonderful passing shot on set point.

With the American starting the second set with a confident hold and an immediate break, Alcaraz was on the ropes.

However, he hit straight back and only dropped two more points on his own serve in the second, unforced errors creeping into Paul's game as Alcaraz levelled the contest.

The third set started with three straight breaks of serve, two of them going Alcaraz's way, and the momentum was with the three-time grand slam champion from there.

The world number three pummelled a forehand winner down the line on set point to go 2-1 up, and it was smooth sailing in the fourth as Paul finally wilted, only winning two points on Alcaraz's serve and giving up back-to-back breaks.

Alcaraz will face Daniil Medvedev in the semi-finals after the Russian outlasted top seed Jannik Sinner to win a four-hour classic earlier in the day.

Alcaraz hailed Paul's performance after his victory, saying of his opponent: "He has been playing great tennis on the grass, beating great players, and today was a really difficult match for me. 

"It was like playing on clay, with big rallies – 10 or 15 shots every point. I had to stay strong mentally, and I'm really happy I could find the solutions."