Giraldo, who was the runner-up at the Chilean clay court event in 2011, rallied to best Argentine Martin Alund 4-6, 7-5, 6-3 in a match that lasted just over 2 hours.
Volandri, meanwhile, dispatched Argentina's Leonardo Mayer, 6-2, 6-1 at Club Naval de Campo Las Salinas at Vina del Mar to move on to the second round.
Former world No. 1 Rafael Nadal is expected to make his return to tennis Tuesday at the VTR Open following a seven-month absence due to a knee injury.
He was set to make his debut in the doubles competition with reigning champion Juan Monaco.
Celebrity Families of 2014 [PHOTOS]