Sinner, who said he ran out of steam in the second set, beat the wildly erratic Tomas Machac 6-1, 6-7 (7), 6-3. Alcaraz followed on 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.
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. "Most important (thing) today was trying to get through somehow.
"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 tiebreak. 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, frequently missing with the court wide open.
He handed Sinner the third-set initiative when wild hitting handed the Italian a break to love in the third game.
Even though Sinner frequently flexed and touched his back during the second set, it was Machac, a right-hander, who called a medical time-out for treatment to his left arm, while 3-2 down in the third.
Sinner then held serve twice before breaking to love to wrap up victory in two hours and one minute.
"I hope I can recover as much as I can for tomorrow," said the Italian.
His quarter-final opponent, sixth seed Felix Auger-Aliassime, needed to expend less energy to advance. The Canadian was leading Casper Ruud 7-5, 2-2 when the Norwegian retired.
Alcaraz imperfect
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 opportunities 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 two hours and 23 minutes in his next service game.
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 after the eccentric Kazakh beat Jiri Lehecka 6-2, 7-5.
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."
'Confident and focused'
19-year-old Joao Fonseca reached the quarter-finals of a Masters 1000 event for the first time when he strode to a convincing 6-3, 6-2 win over Matteo Berrettini in Monte Carlo on Thursday.
The Brazilian's last-eight opponent will be world No. 3 Alexander Zverev who dispatched Zizou Bergs 6-2, 7-5.
Fonseca, who is making his first appearance in Monte Carlo, produced some superb tennis to see off an opponent who had thrashed Daniil Medvedev 6-0, 6-0 in the second round.
The teenager is the youngest man to reach this stage in Monte Carlo since Rafael Nadal and Richard Gasquet in 2005, and is the first Brazilian to reach a Masters 1000 quarter-final since Thomaz Bellucci in Madrid in 2011.
He is the second man born in 2006 to reach the quarter-finals at a 1000-level event, after Spaniard Martin Landaluce, who reached the last eight in Miami in March.
"It is super special. I was looking for this result for a long time," Fonseca said on court.
"Of course I want more. I am very confident and focused. I was very happy with the way I fought today. From the beginning, putting a lot of pressure. Playing huge return games and very good serve games. I was putting a lot of pressure and that helps you stay more calm during the match."
The world number 40, who is up five places in the live rankings, took just 73 minutes in the Monaco sun to book his place in the last eight, stamping his ticket with a winning smash on his first match point.
After dispatching Bergs, Zverev praised Fonseca.
"I think clay is his best surface," Zverev said of the Brazilian. "I am excited to play him for the first time. He is a young upcoming talent and I think we will play each other a lot more in the next couple of years."
Zverev, a two-time semi-finalist at the tournament, ruled the opening set against Bergs as the Belgian struggled on his own service, holding only once.
Bergs found his serve in the second set, but Zverev managed to break at 3-3.
The German lost his rhythm when he was serving for the match at 5-4. Bergs swinging freely broke to love after committing four unforced errors.
Zverev responded immediately by breaking back. He closed out the match in his next service game with an ace on his second match point to win in 1 hour and 51 minutes.
"(It was) a better match from my side," Zverev said when asked how it compared to his opening-round win on Wednesday in Monte-Carlo, where he rallied from 2-5 in the deciding set to defeat Cristian Garin.
"It was still not perfect. Still far from the level I played in the US, but this is my first clay tournament... I am happy with the level today. We move forward."
The No. 3 player in the ATP rankings, Zverev, is chasing his eighth Masters 1000 crown and will now meet Fonseca for the first time. Last month, Fonseca faced Alcaraz and Sinner for the first time in Miami and Indian Wells, pushing both in narrow defeats.