NEW YORK — In dramatic fashion, Novak Djokovic kept alive his quest for a calendar Grand Slam and a men’s record 21st Grand Slam singles title. Pushed harder by No. 4 seed Alexander Zverev on Friday than any other opponent had pushed him at this year’s U.S. Open, the top-ranked Djokovic relied on his superior conditioning and versatile game to wear down Zverev in a 4-6, 6-2, 6-4, 4-6, 6-2 victory that earned Djokovic a berth in Sunday’s final.

All that stands between Djokovic and the rare calendar Slam — winning all four major titles in one year, last done by Rod Laver in 1969 — is No. 2 seed Daniil Medvedev of Russia, who wore down Felix Auger-Aliassime 6-4, 7-5, 6-2 in the first semifinal contested Friday at Arthur Ashe Stadium.

Medvedev, the runner-up to Rafael Nadal here in 2019, lost the Australian Open final to Djokovic in straight sets this year and so has contributed to Djokovic’s list of Grand Slam victims.

It was the fourth straight match here in which Djokovic lost the first set. But in the three previous occasions — against Kei Nishkori in the third round, Jenson Brooksby in the fourth and Matteo Berrettini in the quarterfinals — he won the next three to advance. Zverev, the runner-up to Dominic Thiem at last year’s U. S. Open, put up a stronger and better fight, at least until he began committing careless errors in the fifth set and got too far behind to recover.

Zverev gained a break for 5-4 in the opening set Friday when Djokovic double-faulted, and Zverev then held serve to win the set on his third opportunity. Djokovic got an early break in the second set and cruised the rest of the way, but the third set featured remarkable rallies that showcased each man’s skills. Zverev won a 53-shot rally with a devastating forehand to save a second set point in the 10th game of the third set, but Djokovic closed it out on his third set point.

Zverev broke for a 2-1 lead in the fourth set with a forehand winner and consolidated the break by holding serve. He closed out the set on his first set point opportunity, setting up the decisive fifth set.

Djokovic ended a riveting, 30-shot rally with a forehand passing winner to get a break in the fifth set and take a 2-0 lead, which he extended to 3-0 by holding serve. Zverev made several unfathomable errors in the fourth game, and Djokovic broke his serve again for 4-0. Djokovic served for the match at 5-1, but Zverev stayed with him and broke his serve. Djokovic got his first match point at 30-40 and ended it there.

The second-seeded Medvedev of Russia reached his third Grand Slam singles event final and second at the U.S. Open by relentlessly wearing down No. 12 seed Auger-Aliassime of Canada in a 6-4, 7-5, 6-2 victory at Arthur Ashe Stadium.

Medvedev was opportunistic and solid in earning a spot in Sunday’s final against Djokovic. Medvedev has lost only one set in getting this far, dropping the third set of his quarterfinal match against Botic van de Zandschulp.

Medvedev had to fend off two set points in the second set against Auger-Aliassime but escaped both times thanks to a couple of timely shots and some mistakes committed by the 21-year-old Auger-Aliassime.

Medvedev reached the Australian Open final this year, losing to Djokovic in straight sets. In the 2019 U.S. Open final, Medvedev came back from two sets down against Nadal to force a fifth set, but Nadal held him off.

“It was a strange match a little bit in the second set,” Medvedev said of Friday’s match. “I think everybody thought it would be 1-1.”

In saving those two set points, Medvedev said he was able to turn the match around. But he wasn’t sure at the time he could pull it off. He said his overriding thought was, “Don’t make an ace on the line, please. I’m going to make you play.”

Auger-Aliassime was the first Canadian man to reach the singles semifinals of the U.S. Open since the tournament began in 1881. He struggled with his serve early — he committed 10 double faults in the match — but stayed with Medvedev until the seventh game of the first set. Medvedev then got a break after a series of unforced errors by Auger-Aliassime and held at love to consolidate the break. Auger-Aliassime held serve in the next game, but Medvedev served for the set and finished it out with an ace. The set took only 38 minutes.

The second set stayed on serve until the sixth game, when Auger-Aliassime got the break after Medvedev netted a backhand and then double faulted. That put Auger-Aliassime ahead 4-2, and he held serve for 5-2.

But Medvedev made an impressive comeback. He won the next game at 15 and survived two set points to break Auger-Aliassime in the ninth game, getting the break when Auger-Aliassime sent a backhand wide.

Medvedev pulled even at 5-5 as Auger-Aliassime began to fade. Medvedev broke Auger-Aliassime at love for 6-5 and clinched the set on his second set-point opportunity with an ace.

The third set was almost a formality, as Auger-Aliassime seemed to have little energy left — certainly not enough to come back against Medvedev. Auger-Aliassime committed 39 unforced errors to 25 for Medvedev.

“I don’t think I played my best, but I’m happy to be in the final,” said Medvedev, whose plans included watching from the comfort of his hotel room while Djokovic and Zverev squared off.

In the men’s doubles final, No. 4 seeds Rajeev Ram of the U.S. and Joe Salisbury of Britain defeated the No. 7 duo of Jamie Murray of Britain and Bruno Soares of Brazil, 3-6, 6-2, 6-2.

In a women’s doubles semifinal, Samantha Stosur of Australia and Shuai Zhang of China defeated Desirae Krawczyk of Palm Desert, California, and Alexa Guarachi of Chile, 6-2, 7-5.

Krawczyk and Joe Salisbury of Britain advanced to the mixed doubles final with a 7-6 (2), 6-4 semifinal victory over Jessica Pegula and Austin Krajicek.

Earlier this year, Krawczyk and Salisbury teamed to win the French Open mixed doubles title. Krawczyk won the Wimbledon mixed doubles championship with Neal Skupski.