Two other employees will be laid off for one month without pay.
The video, shot by WJBK-TV, Detroit, at Chrysler's Jefferson North Plant, where the U.S. automaker produces Jeep Grand Cherokees, was aired last week. Chrysler had suspended the workers indefinitely without pay Thursday, the news Web site MLive.com reported.
An employee had tipped off the TV station, saying the workers bought alcohol at a nearby liquor store and smoked in the park.
In a statement about the firings, Chrysler did not refer to the drinking and smoking incident, saying only that the workers violated its standards of conduct.
"As is evidenced by the swift action taken in this matter, it should be clear that Chrysler Group will not tolerate such behavior and will continue to evaluate its protocols to ensure that something like this does not happen again," the company's release stated.
The United Auto Workers said the 13 workers "do not represent the vast majority of workers at Chrysler who do a great job making high-quality vehicles in some of the most productive manufacturing facilities in the United States."
Copyright 2010 United Press International