Novak Djokovic again fought back from a set down to beat Matteo Berrettini 5-7 6-2 6-2 6-3 and move into the US Open semi-finals, the Serb now just two wins away from a 21st major that would complete a calendar-year Grand Slam.

Djokovic, who also lost the opening set in his previous two matches, and Berrettini have met only three times but two were this year when the stakes were at their highest - the Wimbledon final and French Open quarters - with the world number one winning both times in four sets.

The 25-year-old Italian had a third shot at derailing Djokovic's Grand Slam plans on Wednesday but once again could not seize his chance, converting just one of five break opportunities, that coming in the first set.

Djokovic takes another step up in class in the next round, where he faces fourth seed Alexander Zverev, the player who last month ended his bid for a Golden Slam by beating him in the Tokyo Olympics semi-finals.

Djokovic said on court: "He's in tremendous form, he’s been winning a lot. He has comfortably moved to the semi-finals here.

"I know his game well, we played in Tokyo. He’s one of the best players in the world, but the bigger the challenge the more glory in overcoming it.

"This was a great match, with a lot of energy on and off the court. Matteo is a terrific player and every time we face each other it’s a close battle.

"When I lost the first set I managed to forget about it and move on. I was locked in at the start of the second and it was the best three sets I’ve played so far."

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Zverev cruised into the semi-finals with a straight sets win against South Africa's Lloyd Harris

Fourth seed Zverev was untroubled after clinching a tight first-set tie-break and edged closer to a second successive final appearance at Flushing Meadows by defeating Harris 7-6 (8-6) 6-3 6-4 in two hours and eight minutes.

Harris, playing in his first quarter-final at the majors, went toe to toe with Zverev in the first set, breaking the German's serve to take a 5-3 lead and then serving to go one set up.

But Zverev broke straight back and, after both players had held serve to force a tie-break, he kept his nerve as the tension mounted to win 8-6, despite two mini-breaks against him.

Zverev pounced again on Harris’ serve to open up a 3-0 lead in the second set and sealed it 6-3 with his first set point after 36 minutes.

Harris was broken in both his next service games to trail 4-0 in the third set and appeared to lose heart as Zverev closed in on victory.

World number 46 Harris then rallied to extend the match. He broke Zverev for the second time to trail 4-2 and hauled himself back to 5-4, but it was a brief recovery.

Zverev, who let slip a two-set lead to lose to Dominic Thiem in last year’s final, avoided further scares, sealing victory on serve with his first match point.