"This is a very important victory, Cuevas is a good player who is coming from the qualifying rounds, he played a great first set but I was able to take him down," said Chela, who is ranked 162nd and came to Acapulco with a wild card.
Chela, a winner here in 2001 and 2007, has won only two other titles -- at the Netherlands in 2002 and Portugal in 2004.
"I like Mexico very much, people is very nice and I love the surface," Chela said. "Right now I'm not thinking about a victory, it's a long road."
Chela, 29, will play against the winner of Tuesday's match between No. 5 seed Jose Acasuso and Brian Dabul.
Sixth-seeded Alberto Montanes had a comfortable 6-1, 6-4 win over Mexican Bruno Echagaray in the late match and will next play fellow Spaniard Daniel Gimeno Traver, who beat Ecuadorean Nicolas Lapentti, 6-4, 5-7, 6-3.
In other men's matches, Brazilian Thomaz Belluci beat Nicolas Devilder of France 3-6, 6-4, 6-4, Leonardo Mayer defeated fellow Argentine Diego Junqueira 7-6, 6-3 and Italy's Potito Starace eliminated Spain's Oscar Hernandez 6-4, 6-2.
In women's matches, fourth-seeded Iveta Benesova of the Czech Republic had an easy win over Ukrainian Olga Savchuk 6-2, 6-0, while Czech Klara Zakopalova beat 2006 Acapulco champion Emilie Loit of France, 4-6, 6-4, 7-5.
Petra Cetrovska of the Czech Republic beat Spain's Lourdes Dominguez Lino 6-2, 6-2, Italian Tathiana Garbin defeated Jill Craybas of the United States 7-6 (7), 4-6, 6-3 and Roberta Vinci of Italy had a 6-4, 6-4 victory over Lucie Safarova of the Czech Republic.