Another supposed Roland Garros supershow from the Spaniard ended up turning into a bit of a Friday fright night for him on Philippe Chatrier too before he could finally subdue the stubborn Bosnian 6-1 6-3 4-6 6-4 in another compelling contest.
After two sets of his familiar dazzling brilliance, Alcaraz was suddenly dragged into a fierce arm-wrestle with a 33-year-old who needed a medical timeout to an injured leg in the third set yet still reemerged punching to take the champion into a compelling fourth set.
In the fourth, Dzumhur broke at the start for another 2-0 lead, with Alcaraz having become increasingly scrappy and uncharacteristically snappy with his players' box. Yet at 3-1 down, the real Alcaraz rematerialised as he conjured up some wonderful fare to win his 18th clay-court match in 19 played this past two months.
"I didn't enjoy it that much," admitted the 22-year-old, even though everyone else did.
"The first two sets were under control, playing great, feeling great. He played more aggressively, I got down on my energy and it was difficult to push myself. Then I had to fight and give everything I had inside, and I was proud to get the win in the end."
It was the second match running that he'd conceded a set, following his four-set win over Hungarian Fabian Marozsan, but he still appears to have that extra gear that he'll need against 13th seed Ben Shelton in the fourth round.
The American Shelton had earlier swept aside qualifier Matteo Gigante, the Italian who had knocked out Stefanos Tsitsipas, with a 6-3 6-3 6-4 win.
Hopes for a home success were finally dashed when their brightest young talent Arthur Fils, the 14th seed, had to pull out of the tournament with a back injury, scuppering what had looked a rip-roarer against No.17 Andrey Rublev on Saturday.
Earlier on Chatrier, 10th seed Holger Rune demanded a fan to be removed during his see-saw 4-6 6-2 5-7 7-5 6-2 win over French player Quentin Halys, the Dane saying the spectator had shouted aggressively at him because he'd thrown down his towel in frustration at one point.
"The guy was yelling aggressive with me, he reached out for me," explained Rune.
"I thought this was very strange, because I did not do anything against him and he should not interact with a player on the court. It's a bit embarrassing.
"I told the supervisor that I would prefer him not being there, because it was a bit uncomfortable. They said they'd check the video, and if it was true what I said they would get him away. I guess they checked, and I didn't see him for the rest of the match."
Rune's next clash against eighth seed Lorenzo Musetti, who beat Argentine Mariano Navone 4-6 6-4 6-3 6-2, looks set to be one of the most compelling in the last 16.
The suggestion that Novak Djokovic gets what Novak Djokovic wants was shown to be well off the mark as organisers snubbed the great man's plea to be spared playing against Austrian Filip Misolic in Saturday's night session so he could watch the Champions League final between Paris Saint-Germain and Inter Milan on the box.
Alas for the 24-time grand slam champ, tournament bosses turned a deaf ear.
"There will be 15,000 people here so we want to give them the best possible match," said tournament director Amelie Mauresmo.
