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.
"I started off a little slow in the first set," Isner said. "I told myself the only thing I could do was keep fighting. I felt like I was serving well, so just try to hold serve as best as I could. That's what I did."
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 him 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 and aren't scheduled to play their opening matches until Wednesday. Two-time champion Andy Murray is not playing in Shanghai this year after undergoing back surgery last month.
Isner's match was one of only a few that could be completed because of heavy winds and rain from the remnants of Typhoon Fitow, which made landfall in southern China over the weekend and blew through Shanghai on Monday.
Isner played under the roof in the main stadium. In the only other singles matches completed, 11th-seeded Tommy Haas beat American Sam Querrey 6-4, 6-4 without facing a break point, France's Gael Monfils defeated Japanese qualifier Tatsuma Ito 6-3, 6-2 and Spain's Marcel Granollers ousted Serbia's Janko Tipsarevic 6-4, 6-4.
In doubles, Federer teamed with China's Zhang Ze to beat Kevin Anderson of South Africa and Dmitry Tursunov of Russia 6-2, 6-1 in a first-round match.