Briton Murray lost his opening service game and could not cope with the power and accuracy of his Colombian opponent who comfortably won the first set.
There was no change in momentum in the second and Giraldo, who reached the Barcelona final last month, next takes on Roberto Bautista Agut who beat Lukasz Kubot 6-4 6-2.
"I expected a tough match for sure but not the game finishing like that. You go into each match obviously believing you will win," Murray told a news conference.
"It's tough because some days right now I'm playing well and then the next I'm not playing well at all. So yes I need to become more consistent.
"Its not that I necessarily need to go out and practise loads of stuff on the court. I need to be mentally stronger and mentally more switched on."
Spanish world number one Nadal is used to rolling over opponents on clay but this year he lost in the quarter-finals in Monte Carlo and Barcelona to dent his confidence ahead of his bid for a ninth French Open title.
The three-times champion started well and swept Nieminen aside in the first set with a series of powerful passing shots.
Nadal led 3-0 in the second set before Finn Nieminen, the world number 57, broke back and had break points in Nadal’s next service game which he failed to take.
Nadal struggled with his timing but scraped through and next faces sixth seed Tomas Berdych who beat Grigor Dimitrov 3-6 6-3 6-2.
“At 6-1 and 3-0 I was playing at my best level since Monte Carlo but then I slowed down a bit and made some errors,” Nadal told a news conference.
“I am working on finding my level and performance. Today I did what I had to do but I still need to be more consistent.”
Barcelona Open champion Kei Nishikori of Japan reached the quarter-finals after beating eighth seed Milos Raonic 7-6 7-6, his eighth successive victory on clay.
(Reporting by Tim Hanlon, editing by Ed Osmond)
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