On March 23, 1973, he made his debut, beating Martin Munoz by a decision in six rounds. He won twelve fights in a row before drawing (tying), with Nelson Munoz, on December 13, 1973. In 1974, he tasted defeat for the first time, knocked out in seven rounds by Alfredo Alcayaga. In October 11 of that same year, he and Alcayaga had a rematch, this time with the Chilean national flyweight title on the line. Vargas avenged his first defeat, with a seven round knockout win. One month later, he had his first fight abroad, a ten round draw with Carlos Escalante in Buenos Aires.
After fourteen wins in a row, Vargas had a chance to add the South American regional belt to his resume, and he did so by knocking out Gonzalo Cruz in round one, December 20, 1975, in Santiago. He defended that title twice, and after beating Carlos Escalante in their Uruguay rematch, Vargas' win streak reached 27 wins in a row.
On September 17, 1977, he fought for the world title for the first time, WBC world flyweight champion Miguel Canto defeating Vargas by a fifteen round decision in Yucatan, Mexico. Vargas had one more win, and, two months after their first fight, Vargas once again challenged Canto, this time in Santiago. Canto broke the hearts of most Vargas fans on November 30, 1977, by defeating the hometown favorite, again by a fifteen round decision.
On April 22 of 1978, Vargas beat future world champion Alfonso Lopez of Panama by knockout in round one to defend his South American title with success. On November 4 of that year, he challenged WBA world champion Betulio Gonzalez in the champion's hometown of Maracay, Venezuela, but Gonzalez retained the crown with a twelfth round knockout victory.
This defeat was followed by thirteen wins in a row, including points wins over future world champions Joey Olivo and Rafael Pedroza (cousin of Eusebio Pedroza). Vargas then travelled to Japan, where on June 1, he lost what turned out to be his last world title bid, to WBA world Jr. flyweight champion Yoko Gushiken, by a knockout in round eight.
After the Gushiken fight, Vargas had a rather ordinary record of 21 wins and 7 losses before retiring for the first time, in 1987. He did, however, add another regional title to his trophy case, when he beat Delis Rojas, July 23, 1982 by a decision in twelve rounds at Miami, to earn the WBC's continental Americas' flyweight title.
Having retired, Vargas' legend continued growing among Chileans, many of whom spoke of the many times Vargas seemed to be close to become Chile's first world boxing champion. He is still seen by many as the best boxer ever to come out of that country, and as a national hero of Chile.
Ten years after his original retirement, in 1997, Vargas attempted a comeback. His first fight back was videotaped by a crew making a documentary film about him, and he defeated Geronimo Rojas by a knockout in round two on July 4. On February 7, 1998, he added the Chilean Super Flyweight title to his collection of regional titles with a first round knockout over Jose Carmona. One month later, he beat Juan Lielmil, also by knockout in round one, to regain the Chilean flyweight title. But after losing to Joel Garcia, by knockout in round one on July 31 of that same year, he decided to retire permanently.
Vargas had a record of 92 wins, 15 losses and 3 draws, his 62 knockout wins making him a member of the exclusive group of fighters who have won 50 or more fights by knockout. In addition to the documentary about his comeback, a biographical movie about him was also produced in Chile.