The Scot wasted little time in asserting his dominance on the match as he broke his Colombian opponent in just the second game.
From then on, Murray was in cruise control as he eased into a 5-1 first-set lead courtesy of some clever stroke play and several errors from Giraldo.
The world number four wrapped up the first set in just over half-an-hour and took that momentum into the second by breaking in the opening game.
Giraldo responded by surprisingly breaking back to level at 2-2 but Murray took control once again with consecutive breaks on the Colombian's serve.
He then served out the match with ease to set up a last-eight meeting with Milos Raonic, who earlier beat Nicolas Almagro in straight sets.