The American 14th seed was able to dodge heavy rain and swirling winds under the closed roof as a typhoon hit the Qizhong Tennis Centre, but he struggled to impose himself on the 83rd-ranked Colombian.
The 6ft 10in Isner - renowned for his heavy serve - lost the first set 6-4, before wrestling his way back in the second, winning 7-5 after finally taking a seventh set point.
Isner, who fired 29 aces, broke Giraldo in the 12th game of the decider to take it 7-5 and progress to the second round.
It was an easier ride for Frenchman Gael Monfils, who dismissed Japanese qualifier Tatsuma Ito 6-2 6-3 to reach the next stage, where he will face the winner of the match between Richard Gasquet and Vasek Pospisil.
Earlier in the day, Spain's Marcel Granollers was a 6-4 6-4 winner over Serbian Janko Tipsarevic, who struggled his way through with a left ankle problem. Granollers will now meet top seed Novak Djokovic.
Last out on court was 11th seed Tommy Haas, who defeated American Sam Querrey 6-4 6-4.
The top eight seeds - including Djokovic, Rafael Nadal and Roger Federer - all have a bye through to the second round.