Andy Murray, playing his first event since splitting with coach Miles Maclagan, struggled with his serve throughout.
The Scot made just 42% of his first serves, well below the figure normally expected of a top player.
But Falla could not take advantage as the Scot won 7-6 (7-3) 6-1 to set up a semi-final clash with Feliciano Lopez.
Murray revealed that he felt better after his win over Falla than in the previous round when he needed three sets to beat America's Tim Smyczek 6-1 4-6 6-2.
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