Third seed Djokovic ended the surprise run of Peruvian outsider Juan Pablo Varillas, winning 6-3, 6-2, 6-2, and has yet to drop a set through four matches.
The Serb, chasing a third Roland Garros crown, is into a record 17th French Open quarter-final after making the last eight at a major for the 55th time.
“I’m proud of it, but my attention is already in the next match,” said Djokovic, who faces Russian 11th seed Karen Khachanov for a place in the semi-finals, where Alcaraz could await.
“I know what my goal is here. I’m trying to stay mentally the course and of course not look too far.
“Obviously the performance of today gives me a great deal of confidence about how I felt, about how I played.”
Varillas, 27, was the first player from Peru to reach the second week of a Grand Slam since Jaime Yzaga made the US Open quarter-finals 29 years ago.
Djokovic raced 4-0 ahead in the opening set only for Varillas to break in the next game and then have a chance to get back on serve in the seventh game.
But once Djokovic held for a 5-2 lead it was plain sailing for him as he closed out victory in just under two hours.
Khachanov made his third successive Grand Slam quarter-final after he recovered from a bad start to overcome Lorenzo Sonego 1-6, 6-4, 7-6 (9/7), 6-1.
Djokovic holds an 8-1 record against Khachanov, winning their only previous meeting at the French Open in 2020.
Alcaraz looked every part the tournament favourite as he dismantled the talented Musetti in straight sets to return to the French Open last eight.
Musetti had not lost a set in three rounds but Alcaraz brushed the Italian 17th seed aside in barely two hours, triumphing 6-3, 6-2, 6-2 to avenge last year’s defeat on clay in the Hamburg final.
“I think I played such a great level, really high quality of shots. I played a really complete match from the first ball until the last and I’m pretty happy to get through this tough round,” said Alcaraz.
The 20-year-old faces a tough next assignment in 2021 runner-up Stefanos Tsitsipas, who eased past Austrian qualifier Sebastian Ofner 7-5, 6-3, 6-0.
“The clash we’ve been all waiting for,” said Tsitsipas, the Greek fifth seed who has lost all four meetings with Alcaraz. “I think everyone was expecting it, weren’t they? And it’s here. It’s game on.”
– Sabalenka tested but moves on –
Aryna Sabalenka beat 2018 finalist Sloane Stephens 7-6 (7/5), 6-4 in a topsy-turvy encounter in the night session — the first women’s match to feature in the primetime slot this year.
Australian Open champion Sabalenka surged into a 5-0 lead in the opener but Stephens saved four set points as she reeled off five games on the bounce to level.
Second seed Sabalenka eventually edged the tie-break and again held off Stephens in a tight second set to continue her best run in Paris.
The Belarusian goes into a politically-charged duel with Elina Svitolina who, playing her first Grand Slam since becoming a mother, reached the quarter-finals for the fourth time.
The Ukrainian defeated Daria Kasatkina 6-4, 7-6 (7/5) for a seventh win in seven meetings against the Russian who was a semi-finalist last year.
As with all her matches, Svitolina opted not to shake hands with her Russian opponent in protest at the war in Ukraine. Belarus is also a key military ally of Moscow.
Kasatkina still gave her rival a friendly thumbs-up.
Anastasia Pavlyuchenkova, the 2021 runner-up, rallied from a set and a break down to dump out Belgian 28th seed Elise Mertens 3-6, 7-6 (7/3), 6-3.
The Russian, whose ranking has plunged to 333 after a serious knee injury, is the lowest-ranked Grand Slam quarter-finalist in the tournament’s history.
Pavlyuchenkova will take on Karolina Muchova for a place in the last four after the Czech saw off lucky loser Elina Avanesyan 6-4, 6-3.
mw/dj