The big-serving Isner had 18 aces but Mello converted the only break point of the first set to take control of the match. The Brazilian then saved four of the five break points he faced in the second before prevailing in the tiebreaker against last year's finalist.
The 30-year-old Gonzalez dominated the first set, although both players struggled to hold serve in the second. Klizan double-faulted on Gonzalez's second match point.
Lopez made the decisive break in the 11th game of the second set on a wind-swept day at the ATP tour event organized by the family of Novak Djokovic.
"To beat Monaco on clay, you have to be confident," Lopez said.
Ungur will play the second-ranked Djokovic, who is opening his clay-court season Wednesday after winning 24 consecutive matches this year. He won titles at the Australian Open and hard-court tournaments in Dubai, Indian Wells and Miami.
It's his first tournament back since he pulled out of the Monte Carlo Masters with a knee injury on April 8.