PARIS, May 25 (Xinhua) -- Alexander Zverev and Carlos Alcaraz had to save match points to come back from the brink to stay on track for a maiden Grand Slam title at Roland Garros, while the "Big Two" of Rafael Nadal and Novak Djokovic advanced with comfortable victories in the French Open on Wednesday.

Newly-crowned Madrid Masters champion Alcaraz came to Paris as one of the title favorites after beating Djokovic and Nadal in recent weeks. But the youngster had a tough match against his compatriot Albert Ramos-Vinolas in the second round, rallying to win 6-1, 6-7 (7), 5-7, 7-6 (2), 6-4 after over four and a half hours.

Ramos-Vinolas, who is 15 years older than Alcaraz, was clinical in the second and third sets, while the No. 6 seed committed too many unforced errors during this period.

The 19-year-old even had to save a match point in the fourth set when trailing 5-4 behind on Ramos-Vinolas' serve, but he pulled through.

"That match point changed everything," Alcaraz said.

With almost the full support from the audience at Simonne-Mathieu court, Alcaraz regained his confidence and showed relentlessness in the tie-break of the fourth set, dragging the match to a decider.

"It was a great battle against a great player. I knew it would be a top match," said Alcaraz. "I felt fresh in the fifth set, like the beginning of the match."

He secured a decisive break in the ninth game of the last set, before serving out the match to love to complete a rollercoaster victory.

"I feel tired," was Alcaraz's first answer when asked how he felt about the match.

Next up for Alcaraz is fellow rising star Sebastian Korda, who dispatched local veteran Richard Gasquet in straight sets 7-6 (5), 6-3, 6-3 later on Wednesday.

Third-seeded Zverev was another high-ranked player who had a scare in the second round, as the German dug himself out of a deep hole to come back from two sets behind and overturn Argentina's Sebastian Baez 2-6, 4-6, 6-1, 6-2, 7-5 to avoid an early exit.

"I'm happy still being in the tournament right now," said last year's semifinalist, who saved a match point on serve at 5-4 in the final set.

"I was planning my holiday in Monaco, where I was going to go and who I was going to with that help me relax, thinking about the beach," the 25-year-old joked after the match.

"You just have to find a way. Like Rafa, Roger and Novak, they always find a way."

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

The two-time ATP Tour Finals champion will face the U.S.'s Brandon Nakashima in the third round.

Nadal, the 'King of Clay', celebrated his 300th Grand Slam win by beating French wildcard Corentin Moutet at the Philippe-Chatrier court.

The 13-time French Open champion showed no mercy to the 23-year-old, who regarded Nadal as a childhood idol, wrapping up the victory 6-3, 6-1, 6-4 in just over two hours.

The 35-year-old fifth seed has been troubled by a chronic foot injury in recent months, but landed at Roland Garros in good form.

"The last couple of months haven't been easy. The victories help a lot," said the Spaniard.

Defending champion Djokovic, seeking a record-equalling 21st major title, blasted into the round of 32 after defeating Slovakia's Alex Molcan in straight sets 6-2, 6-3, 7-6 (4).

On the women's side, last year's semifinalist Maria Sakkari of Greece suffered a shock defeat to the Czech Republic's Karolina Muchova 7-6 (5), 7-6 (4).

Sakkari's loss saw another women's seeded player edged by a dark horse at the clay major this year, following the first-round exits of top ten seeds Barbora Krejcikova, Anett Kontaveit, Ons Jabeur and Garbine Muguruza.