Carlos Alcaraz and Alexander Zverev saved match points to fight back from the brink and reach the French Open third round.

That came after German third seed Zverev sealed a 2-6 4-6 6-1 6-2 7-5 win over Argentine Sebastian Baez.

By contrast, Novak Djokovic and Rafael Nadal both swept past their opponents.

Serbia's defending champion Djokovic beat 38th-ranked Slovak Alex Molcan 6-2 6-3 7-6 (7-4), while Spanish 13-time winner Nadal defeated Frenchman Corentin Moutet 6-3 6-1 6-4 for his 300th Grand Slam match win.

Alcaraz, among the favourites at Roland Garros after victories over Djokovic and Rafael Nadal in recent weeks, produced some outrageous shots as he battled past Ramos-Vinolas.

He was supported by a full-throated crowd on Court Simonne-Mathieu as he saved a match point in the fourth set before finding an extra gear to take victory after four hours.

"I feel tired," was the 19-year-old's first answer when asked how he felt about his win.

Alcaraz's victory came after Zverev, a semi-finalist at Roland Garros last year, had fought past his own emotions to secure victory.

The German roared to the crowd in celebration before putting his arm around Baez at the net and speaking to him at length.

"I told Sebastian this is the worst you will ever feel on a tennis court, right now at this moment," Zverev said.

"I know how he feels as I lost the US Open final from being two sets up and was two points away."

Zverev joked that mentally planning his post-French Open holiday helped him relax after a poor start.

"I couldn't have played any worse [at the start], I just tried to find a rhythm and did that," he said.

"I was planning my holiday in Monaco, where I was going to go and who I was going to go with and that relaxed me, thinking about the beach."

'That match point changed everything'

At four hours and 34 minutes, this was the longest match of Alcaraz's young career, with the teenager having to fight back from a break down in both of the final two sets.

He produced some delightful moments, including to secure the decisive break in the final set.

For three consecutive shots, Alcaraz was almost hit off the court, scrambling back and forth, but somehow managed to retrieve the ball before Ramos-Vinolas dumped a volley into the net.

Ramos-Vinolas threw his racquet in frustration and then watched Alcaraz serve out the match to love to complete a fine victory.

"It was a great battle against a great player. I knew it would be a top match," Alcaraz said.

"In the fifth set I was fresh. I was like the beginning of the match. That match point changed everything."

'Rafa, Roger & Novak always find a way'

Olympic champion Zverev has said he believes he will form a "new big three" alongside Djokovic and Daniil Medvedev.

However, Zverev is the only one of the three not to have won a Grand Slam and came perilously close to an early exit on the Paris clay.

He shouted at his camp and was booed by the crowd for making a hand gesture towards him after a double fault that saw him trail by a set and a break against Baez.

He initially struggled to hit through the world number 36 but began to show more form as the match went on, fighting back from 4-0 down in the second set before losing it 6-4.

He broke Baez's serve to start the third set and both his serve and backhand improved throughout the three hour 36 minute match.

"I'm happy still being in the tournament right now," Zverev said in his on-court interview.

"You just have to find a way. You talk about mental strength and the greats, like Rafa [Nadal], Roger [Federer] and Novak, they always find a way.

"I will never be at their level but I'm trying to get closer to them."

Zverev will play American Brandon Nakashima next.

Djokovic beats former coach's new charge

World number one Djokovic hit 10 aces and 40 winners to 19 unforced errors as he aimed to keep his time on court at a minimum in a 6-2 6-3 7-6 (7-4) win.

His opponent Molcan is coached by Marian Vajda, who worked extensively with Djokovic during the Serb's rise to the top of the world rankings and his 20 Grand Slam titles.

Giving his post-match interview in French, Djokovic thanked the crowd on Court Suzanne Lenglen for their support.

"I don't have a lot of opportunities to play here, and I could feel the support," said the 35-year-old, who plays Slovenia's Aljaz Bedene next.

"There were tricky conditions today with a lot of wind coming in different directions, I had to stay focused."

In the night session on Court Philippe Chatrier, record 21-time Grand Slam champion Nadal dominated the first two sets against 23-year-old Moutet before holding off his resurgent opponent in the third.

Seeking a record-extending 14th title at Roland Garros, the Spaniard once again appeared untroubled by the chronic foot injury which had affected him at the Italian Open earlier in May in another classy display.

The 35-year-old fifth seed wrapped up a second successive straight-set win in Paris to record his 107th French Open victory, and set up a third-round meeting with Dutchman Botic van de Zandschulp.

"The last couple of months haven't been easy. I had to be off the court for a while, so it's day-by-day work," Nadal said.

"I'm enjoying the fact I am at Roland Garros - the most important tournament of the year for me. Let's see what can happen."

Elsewhere, Canadian ninth seed Felix Auger-Aliassime defeated Argentine Camilo Ugo Carabelli 6-0 6-3 6-4.

Spaniard Bernabe Zapata Miralles came back to stun American 13th seed Taylor Fritz 3-6 6-2 6-2 6-3, while Argentine 15th seed Diego Schwartzman avoided a huge scare as he recovered from two sets down to beat Spain's Jaume Munar 2-6 6-7 (3-7) 6-2 6-2 6-2.