Robredo will meet fourth-seeded Jose Acasuso for a place in Sunday's final. Pablo Cuevas of Uruguay will play either defending champion Fernando Gonzalez or Juan Monaco.
At 3-3 in the final set, Robredo made the decisive break against Chela.
The Spaniard was through to his first semifinals since he won his seventh ATP title last July at Bastad, Sweden.
He had a 3-2 record against Acasuso.
Acasuso, the 2006 champion, won 6-4, 6-2 against fellow Argentine Sebastian Decoud, a lucky loser who reached his first tour quarterfinals.
Acasuso was playing in his first event of the year after missing last month with a right shoulder injury.
Cuevas made it to the last four for the second straight year after beating local wild card Paul Capdeville 7-5, 7-5.
"I'm really happy to reach the semifinals after playing two very difficult matches to qualify and two more difficult matches in the tournament,'' Cuevas said.
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