The 14th-seeded American fought off three break points at 5-5 in the third set, then broke Giraldo for the second time to close out the match.
Isner could meet Rafael Nadal in the third round.
Nadal, seeded second in Shanghai, supplanted Novak Djokovic as the top-ranked player on Monday, despite losing to the Serb in the final of the China Open in Beijing a day earlier.
Djokovic is the defending champion and seeded No. 1 in Shanghai. He could meet Roger Federer in the quarterfinals.
Djokovic, Nadal and Federer all have first-round byes.
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