Alcaraz overcomes slump to reach Wimbledon quarter-finals
The Spanish world number three came through 6-3, 6-4, 1-6, 7-5 against his 16th-ranked opponent to book a spot in the last-eight of a major for the ninth time in just 14 appearances.
However, it was another uncomfortable afternoon for Alcaraz, who had needed five sets to see off Frances Tiafoe in the third round.
His erratic performance on Sunday saw him drop serve five times and commit an uncharacteristic 33 unforced errors.
"Playing lefties is always tricky, no matter the surface," said Alcaraz, who lost to British left-hander Jack Draper at Queen's on the eve of Wimbledon.
"I learnt a little bit from that. I felt great playing today, I think I played a really high level."
The 21-year-old, bidding to become just the sixth man to win the French Open and Wimbledon back-to-back, eased through the first set under the Centre Court roof before crucially saving four break points in the fifth game of the second.
Alcaraz wrapped up the second set despite losing his footing and tumbling towards the ground.
"I just try to fight for every ball, it doesn't matter which part of the court I am, I just try to run in whichever part of the court I am on," said Alcaraz.
"I give myself the chance to stay alive in the point.
"Set point is a really important point for me so I had to show the opponent that whatever shot he shoots, I will be there.
"That's me, I will be there, fighting until the last ball and sometimes it is a good point like this one and sometimes I lose it but the main thing is just to fight."
Despite that dramatic conclusion, Humbert stormed back, breaking the champion three times in the third set as Alcaraz went spectacularly off the boil.
Alcaraz was twice unable to hold onto breaks in the fourth set and had to fend off three break points in the eighth game to stay level at 4-4.
Left-hander Humbert then lost his bearings to hand over a service break in the 11th game and Alcaraz took full advantage to quickly seal the tie.
Alcaraz will take on either American 12th seed Tommy Paul or 36-year-old compatriot Roberto Bautista Agut, a semi-finalist in 2019.
