Jannik Sinner and Carlos Alcaraz both suffered second-set stumbles on Thursday in their race for the No 1 ranking but recovered to reach the last eight of the Monte Carlo Masters.
Sinner, who said he ran out of steam in the second set, beat the wildly erratic Tomas Machac, 6-1, 6-7 (3/7), 6-3.
Alcaraz followed Sinner on to the centre court and his match went to a similar pattern before he beat Tomas Etcheverry 6-1, 4-6, 6-3.
Alcaraz, the defending champion, could lose the No 1 ranking to Sinner, who was finishing a ban last year and has no ranking points to lose this week. The Italian came into Monaco after winning the Masters tournaments in Indian Wells and Miami.
On Thursday, Sinner galloped through the first set but slowed in the second, allowing Machac to hit his way back into the match.
"I was struggling a little bit, was a bit tired," Sinner said.
"I felt great before the match, in the second set I struggled a bit with trying to find the right energy. This can happen. I tried to push myself through which I've done."
Machac squandered two set points on serve at 5-4 in the second but then romped through the tie-break.
That ended Sinner's record streak of 36 straight sets in 1000-level events but he stayed cool to stretch his run of Masters wins to 19.
Even with his opponent struggling, the Czech kept flailing for winners. He handed Sinner the third-set initiative when wild hitting handed the Italian a break to love in the third game.
Sinner held serve twice before breaking to love to wrap up victory in two hours and one minute.
His quarterfinal opponent, sixth seed Felix Auger-Aliassime, needed to expend less energy. The Canadian was leading Casper Ruud 7-5, 2-2 when the Norwegian retired.
"I hope I can recover as much as I can for tomorrow," said Sinner.
Alcaraz also blazed through the first set.
"I was hitting the ball really well in the first set, like ten out of ten," said the Spaniard.
But in the second he made 23 unforced errors.
"I had the chance to break his serve in the second set and I didn't take it and every time you don't take the opportiunities at this level you have to run back," said Alcaraz.
"He gained a little confidence, played more aggressive, hitting the ball better."
Alcaraz re-established control when he broke in a marathon second game in the final set but was struggling to put his first serves in play.
The top seed saved a break point to go 5-2 up and then needed three match points to clinch victory in 2hr 23min in his next service game.
'IT'S GOING TO BE FUN'
Alcaraz said his troubles had a lot to do with his opponent.
"Especially on clay he's a great fighter," Alcaraz said. "It's been a great day, a great battle."
The Spaniard will next face Alexander Bublik for the first time.
Kazakh Bublik, who beat Jiri Lehecka 6-2, 7-5, is, like Alcaraz, known for his drop shot.
Alcaraz said the two men had practised together.
"It's going to be fun to play," he said. "Let's see who has the best drop shot."
Earlier, 19-year-old Joao Fonseca reached the quarterfinals of a Masters 1000 event for the first time when he strode to a convincing 6-3, 6-2 win over Matteo Berrettini.
The teenager is the youngest man to reach this stage in Monte Carlo since Rafael Nadal and Richard Gasquet in 2005.
"It is super special," Fonseca said on court. "Of course I want more. I am very confident and focused."
The Brazilian's last-eight opponent will be world No 3 Alexander Zverev.
"I am excited to play him for the first time," Zverev said of Fonseca.
"He is a young upcoming talent and I think we will play each other a lot more in the next couple of years."
Germany's Zverev despatched Belgian Zizou Bergs 6-2, 7-5.