Nalbandian, a member of the Argentinian team that beat Novak Djokovic's Serbia in last month's Davis Cup semi-finals, has slipped to 57th in the world rankings after an injury-plagued season.
But the 29-year-old was too good for his higher-ranked opponent, breaking Gulbis (ranked 51) twice in the first set and then once more in the second set to seal the win.
Later matches feature 10th seed Andy Roddick against Taiwan's Lu Yen-hsun, 16th seed Fernando Verdasco against China's Li Zhe, and Russian Mikhail Youzhny against Spain's Juan Carlos Ferrero, a former world number one.
Top seeds Rafael Nadal and Andy Murray, who met in Sunday's Japan Open final, won by the British player, both have byes into the second round in Shanghai.