The foruth-seeded Greek right-hander lost 6-4 3-6 7-5 in two hours nine minutes as Humbert progressed to a last-16 encounter with American JJ Wolf.
Top seed Carlos Alcaraz also had a tough time but edged past Briton Dan Evans 7-6 (7-1) 6-4 despite trailing by a break in each set. While a set shorter the match lasted 18 minutes longer than Tsitsipas's.
Evans took a set off the Wimbledon champion at the US Open last month and looked like doing so again in a first stanza that lasted an hour and 27 minutes.
Evans led 4-1 but had converted his only opportunity, while Alcaraz could take only one of his 13 break points, with his opponent saving six of them in a fifth game that lasted nearly 20 minutes.
Alcaraz fought back to make it 4-4 and dominated the tie-break but Evans did not allow his head to drop and came out strongly in the second set before eventually succumbing.
"It was one of the toughest matches I've played so far outside of the grand slams," Alcaraz said.
"Every time I face Daniel it's a tricky match. I think both of us played a high quality of tennis. I'm really happy to get through."
Alcaraz will next face 18th-seeded Grigor Dimitrov, who beat 13th-seeded Karen Khachanov 7-6 (8-6), 6-4.
Wild card Diego Schwartzman upset seventh seed Taylor Fritz 6-4 3-6 7-6 (7-5) for his first win over a top-10 player in almost 18 months. The 31-year-old Argentine will next meet 22nd-seeded Nicolas Jarry, who beat Lorenzo Sonego 7-6 (7-4) 6-2.
Fifth seed Andrey Rublev breezed to a 6-3 6-0 win over Adrian Mannarino. He now faces Tommy Paul who beat beat 19-year-old Arthur Fils 6-4 6-7 (5-7) 6-4.
with AP
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