Spaniard Robredo beat Santiago Giraldo of Colombia 6-1 6-4 in the other semi-final.
Murray, who needs a strong finish to his season to qualify for the ATP World Tour Finals, dropped the first set and was 3-3 when he reeled off nine straight games to surge ahead.
"He started the match well," said Murray. "I was struggling a little bit with my timing. Obviously, the conditions were very hard today. But I feel good and I'm into my first final for a while.
"Hopefully it'll be a good match. Robredo's been playing some good tennis this year, so it'll be tough. I'm enjoying myself here and winning always helps," said Murray who underwent a back surgery last year.
Murray, who will need to move three spots up from his current 11th place in the Race to London to qualify for the eight-man finale, dropped just four points on serve in the third set while converting all three break points.
"It's been a tough year for me. The first few months coming back from surgery were hard, then I lost a bit of confidence. But I've felt better the past few months and hopefully I can have a strong end to the season," added Murray.
(Reporting by Amlan Chakraborty,; editing by Pritha Sarkar)
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