Rafael Nadal demonstrated once again why he is the greatest player in French Open history by beating long-time rival Novak Djokovic in a late-night thriller to reach the men's singles semi-finals.

Nadal secured victory at 1:15am local time after over four hours on court.

The 21-time Grand Slam winner now faces third seed Alexander Zverev on Friday.

Germany's Zverev, 25, reached the semi-finals for the second successive year after surviving teenage sensation Carlos Alcaraz's fightback earlier on Tuesday.

"To win against Novak there is only one way: to play your best from the first point to the last," said 35-year-old Nadal, who thanked the Chatrier crowd for showing their "love".

"This is one of those magic nights for me."

Victory for Nadal avenged his semi-final defeat by Djokovic last year and extended his all-time record on the Roland Garros clay to 110 wins in 113 matches.

The rivalry between the pair is the most enduring in men's tennis, with Nadal winning their 59th meeting seeing him narrow the gap to 30-29 in the head-to-head.

"Nadal showed why he is a great champion and stayed mentally tough. No doubt he deserves it," said Djokovic.

"He was the better player in the important moments, he started well and I didn't start so well.

"I gained momentum in the second set and I thought I was back in the game. But he was able to take his tennis to another level."

Fast start pays dividends for Nadal

In front of an adoring crowd, Nadal demonstrated yet again why he is so special on the court where he has enjoyed the greatest successes of his career.

At the end of last year the Spaniard thought he would have to retire because of a chronic foot problem and was hampered by the issue at the Italian Open earlier this month.

A stress fracture of the rib also caused him to miss three months of the season shortly after his record-breaking 21st major win at the Australian Open.

Despite turning 36 later this week, and needing five sets to beat Canada's Felix Auger-Aliassime on Monday, he dug deep into his physical and mental reserves to beat Djokovic.

Nadal blew Djokovic away in fast starts in both of the pair's matches at Roland Garros in 2020 and 2021 and, although those matches ended in different conclusions, the Spaniard set out to do the same this time.

The left-hander played superbly in the first set, pinning Djokovic back in the court and punishing him with fizzing forehand winners.

Nadal took four of his 12 break opportunities, while saving four of Djokovic's five, to win a 50-minute opening set.

Hitting 27 winners compared to 12 unforced errors was a complete contrast to his slow start in the previous round against Auger-Aliassime.

That laid the platform for Nadal to eventually go on to record another memorable victory.

"It was an emotional night and I still play for nights like tonight," said Nadal.

"But it is just a quarter-final and I still have a semi-final to come. I will stay emotionally stable and get ready for the semi-final."

Djokovic unable to take chances

While Nadal has had fitness issues, Djokovic's season has been disrupted by not being allowed to play in the Australian Open and tournaments in the United States because he was not vaccinated against Covid-19.

The 20-time Grand Slam champion looked to be heading towards peak form, winning the title in Rome and then not dropping a set at Roland Garros going into the quarter-finals.

Many had thought playing the match in the colder night-time conditions would also favour the Serb.

Maintaining his sky-high level proved to be the issue for Nadal against Djokovic in last year's semi-final, but the Spaniard broke again and moved into a 3-0 lead in the second set.

While temperatures started to drop, Djokovic began to warm up and fought back to level at 3-3 after a sixth game lasting almost 19 minutes.

Lengthy games with few routine holds continued and the set eventually tipped in the favour of Djokovic when Nadal cracked a forehand long on the second set point.

"He was the better player in the important moments, he started well and I didn't start so well," said Djokovic.

"I gained momentum in the second set and I thought I was back in the game. But he was able to take his tennis to another level."

Nadal broke to love at the start of the third set and moved into a 4-1 lead when a double fault from Djokovic was followed by the Serb dragging a crosscourt backhand wide.

That was Nadal's sixth break of Djokovic's serve from 15 opportunities and he served out for a two-sets-to-one advantage with few problems.

Despite time passing midnight in Paris and temperatures dropping to about 10C, few fans decided to leave Chatrier and many of those who stayed were wrapped up in blankets.

Djokovic broke for a 2-0 lead early in the fourth but missed two set points when serving at 5-3 and was punished when Nadal nailed a crosscourt forehand winner to put the set back on serve.

Most of the 15,000-capacity crowd was supporting Nadal and their patience was rewarded when their man dominated the tie-break to earn a stunning victory.

Nadal led 6-1 in the breaker and took his fourth match point with a driving backhand volley before soaking up the acclaim of a jubilant Chatrier.