French Open: Novak Djokovic and Carlos Alcaraz win quarter-finals to set up semi-final showdown

Novak Djokovic and world No 1 Carlos Alcaraz will face each other in the French Open semi-finals after both came through their quarter-final matches on Tuesday.

Djokovic overcame a first-set blip to beat Karen Khachanov 4-6 7-6 (7-0) 6-2 6-4.

The Serbian, twice champion before at Roland Garros, remains on course for a record-breaking 23rd men's singles Grand Slam title, though he didn't have things all his own way against Khachanov.

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The 36-year-old did not have a single break opportunity in the opener as he ultimately dropped his first set of the tournament.

Khachanov - a semi-finalist at the US Open last September and the Australian Open earlier this year - instead stole Djokovic's serve to lead 3-2 and, although the Serb threatened in a 10-minute ninth game, the 11th seed held and went on to hold out for a 6-4 advantage.

There were no break points for either player in the second set as Khachanov took the world number three to a tie-break, but the Russian began to fade at the crucial moment, failing to score a point as Djokovic levelled the contest.

Djokovic followed that up with an early break of the dejected Khachanov in the third and ended up stealing his serve once more to close in on victory.

The same pattern appeared to be unfolding in the fourth set, with Djokovic again securing an early break, though this time a double fault from the Serb allowed Khachanov to level things up at 4-4.

The 27-year-old failed to convert that break in his next service game, however, being broken to love as Djokovic claimed eight points in a row to swiftly and emphatically conclude the contest, wrapping things up with an ace.

Alcaraz demolishes Tsitsipas to set up showdown

Alcaraz swatted aside fifth seed Stefanos Tsitsipas 6-2 6-1 7-6 (7-5) in the night session to set up the showdown with Djokovic.

On paper this appeared the toughest test for Alcaraz so far but he had won all four previous meetings against Tsitsipas, including in Barcelona in April, and was in total control from the start.

He was better in every aspect and Tsitsipas, who had won all six of his previous slam quarter-finals, simply had no answer to Alcaraz's all-round wizardry, with winners flying past him and drop shots catching him out time and again.

The Greek did not play badly in the opening set but still had his serve broken twice and he appeared to grow increasingly demoralised in the second, where he won only 13 points.

The crowd were torn between admiring the flamboyant brilliance of Alcaraz and wanting a contest, and they responded to Tsitsipas' call for encouragement when he finally won a game at 0-3 in the third set.

Alcaraz threatened to be held up more by a Mexican wave than his opponent but Tsitsipas did at least provide a late challenge, saving two match points at 2-5 and then breaking the 20-year-old for the first time when he served for victory.

A third match point came and went as Tsitsipas forced a tie-break, where he saved a fourth and fifth, but on his sixth chance Alcaraz converted.

Djokovic struggles for rhythm: 'I came in a bit sluggish'

Speaking after his win, Djokovic said: "He [Khachanov] was the better player for most of the first two sets.

"I was struggling to find my rhythm, I came into this a bit sluggish.

"Then I played a perfect tie-break and from that moment onwards I played a couple of levels higher and managed to win eight points in a row to finish it off."

He added: "I missed a couple of easy shots today. These things happen; sometimes it works, sometimes it doesn't.

"He has a big serve but maybe doesn't move as well, so I tried to expose him and played unpredictable.

"It was a big fight but that's what you expect from a Grand Slam quarter-final."

Alcaraz relishing facing Djokovic again

World No 1 Alcaraz said after his win: "Believing in myself all the time, I'd say that's the most important thing. I always feel I'm going to play this kind of matches at this level.

"I lost my focus a little bit at the end of the third set, I had a couple of match points. He started to play I would say better. I was in trouble but I'm really happy to overcome that problem, still playing a great level, believing that I was going to win the third set."

On facing Djokovic, Alcaraz said: "This match everyone wants to watch. I would say it's going to be a really good match to play and to watch. I really wanted to play this match. If you want to be the best you have to beat the best."