Chela dropped just three points on serve to take the first set but was broken in the opening game of the second.
The seventh-seeded Granollers, who was on a seven-match winning streak following his victory in Gstaad last week, got treatment for a sore right arm muscle and lost control of the second set.
"The result looks easy but it was tough. I am happy to win it in straight sets," Chela said.
The 50th-ranked Montanes downed Santiago Giraldo of Colombia 6-1, 7-6 (0) to advance to his second semifinal of the season.
Haase defeated sixth-seeded Andreas Seppi 6-4, 6-2 to reach his second career semifinal. The Dutchman needed eight set points to close out the opening set but converted his first match point against the Italian, who won just two service games.
"I played too defensively from the start but he helped me with some mistakes and I was more aggressive in the second set," said the 53rd-ranked Haase, who reached the semifinals at the Dutch Open in 2007.
Souza, a qualifier ranked 110th, beat No. 8 Pablo Andujar of Spain 6-3, 6-4 to reach his second semifinal of the season after Santiago, Chile, in February.
Earlier Thursday, Haase rallied to beat second-seeded Feliciano Lopez of Spain 1-6, 6-4, 6-3 in a second-round match.
Haase and Lopez were tied at 1-1 in the final set when rain interrupted play on Wednesday. Haase broke Lopez in the first game after resuming and closed out the win when the Spaniard double-faulted on match point.