Etcheverry, nicknamed El Diablo (The Devil), joined D.C. United of Major League Soccer in its inaugural season of 1996, and led the team to three MLS Cups and was named MLS MVP in 1998. In eight years with the team, Etcheverry played 191 league games, scoring 34 goals and registering 101 assists (the games and assists were DC records). He retired at the end of the 2003 season. In 2005, he was named to the MLS All-Time Best XI.
On September 23, 2006, Etcheverry was honored at a home game against the New York Red Bulls. During halftime he was put up on the "D.C. United Tradition of Excellence" sign in the stadium. The only other person on that wall is John Harkes. After all of this Etcheverry walked over to the La Barra Brava part of the stadium and did his trademark clap in front of them, he would do after every game win or lose.
On October 20, 2007, Etcheverry was honored with a tribute match at RFK Stadium, prior to United's regular-season finale versus Columbus. Etcheverry is the first United player to be so honored. Etcheverry, playing with teammates from the club's 1997 MLS Cup winning side, defeated Hollywood United (a collection of former players and actors), 2–1, with Etcheverry drawing and scoring the winning penalty in the final minute.
Etcheverry compiled 71 caps and scored 13 goals for the Bolivian national team between 1989 and 2003. He played for them in the 1994 World Cup, where he is remembered most for getting sent off just minutes after entering the tournament's opening game against Germany for kicking Germany's star player Lothar Matthäus. However, he was a critical part of Bolivia's qualifying campaign for that tournament, scoring an especially vital goal to help Bolivia beat Brazil.
On April 12, 2006, the Bolivian Congress awarded him with the "Order of Merit" and a title of "Distinguished Citizen", for his sport achievements, shortly after his retirement.
Etcheverry made his debut as football coach in early 2009 after he accepted an offer from second division club Sociedad Deportiva Aucas, but he was sacked after only four months in charge. On 6 October 2009, Etcheverry was announced as the new Oriente Petrolero coach, replacing Pablo Sánchez. But in the middle of the negotiations he decided not to go through.