Murray was in control of the match all the way through, breaking Giraldo once in each of the sets and saving the only break point he faced in set 2.
The Brit’s aggressive game proved to be too much for the Colombian, who was forced to move way behind the baseline, Murray stepping in and dictating the rallies.
Next up for Murray will be the Frenchman Richard Gasquet, who eliminated Tommy Haas of Germany 6-7 (3) 6-3 6-0 6-0.
Also through to the last 16 is the 6th seed Spaniard David Ferrer, who outclassed 27th seed Russian Mikhail Youzhny, allowing him only four games in total as he cruised to a 6-0 6-2 6-2 victory.
Ferrer looks as strong as ever and with this win, he surely grabbed the attention of the top four seeds.
The Spaniard could potentially meet Murray in the quarterfinals if they both get through their next round matches.
From the other matches: 8th seed Serbian Janko Tipsarevic also posted a comfortable three sets win, eliminating 29th seed Frenchman Julien Benneteau 6-3 7-5 6-4 and 12th seed Nicolas Almagro joined his Spanish colleagues in the last 16, defeating Leonardo Mayer of Argentina 6-4 6-1 6-2.