Edmund, 21, who this week climbed to a career-best ranking of 48th, beat the Argentine 6-3 5-7 6-4.
The British number two last week reached the quarter-finals of the China Open, which was won by Andy Murray.
Wawrinka, 31, is the third seed in Shanghai and attempting to win his fifth title of 2016.
Britain's Kyle Edmund will face world number three Stan Wawrinka in the second round of the Shanghai Masters, after beating Federico Delbonis.