The Scot, who also beat Robredo in last month's Shenzhen final, won 3-6 7-6 (9-7) 7-6 (10-8) after three hours and 20 minutes.
Murray, 27, claimed his third title in five weeks and closes in on a place at the ATP World Tour Finals. He moves up to fifth in the standings, with ninth good enough to qualify.
"I know it was an incredible match," said Murray. "The tennis at the end and in the second set was high level. I played well at the right moments."
Murray will now head to the Paris Masters, the final event of the regular season, and would need an unfortunate set of results next week to slip out of the places for London.
Whether he will be in any shape to make the latter stages in Paris must be in doubt after winning the longest ATP final of 2014 against Robredo.
In one of the most remarkable matches of his career, Murray overcame bouts of exhaustion and cramp and fought off a succession of match points before finally clinching victory.
Both finalists were playing for the fifth week in succession and Robredo, 32, was similarly affected by fatigue.
It looked as though the Spanish veteran would make amends for a heartbreaking loss against Murray in China last month but in the event history repeated itself, with another five match points slipping by.
Robredo was the more clinical player for much of the contest, converting all four break points compared with two from 13 by Murray, and after taking the first set the Spaniard hauled his way back into the second to force a tie-break.
With victory in his sights, Robredo pushed a nervy forehand wide on his first match point before Murray slammed down an ace on the second.
The former Wimbledon champion grabbed his opportunity to extend the match by reeling off the next two points, forcing a decider and surely wresting the momentum decisively in his favour.
It was never likely to be that straightforward, and with chants of "Tommy! Tommy!" ringing around the arena, both men looked to be suffering with cramp at times.
-BBC
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