Virviescas joined America de Cali's youth ranks in 1994, until making his senior debut in the 1999 season. In 2002, he had a brief loan spell at Real Cartagena. While at America, he won the 2000 and 2001 league titles. In 2003, he joined River Plate for a brief spell which lasted a year, being part of the squad that finished runner up in the 2003 Copa Sudamericana and that won the 2004 Clausura. The following year he moved to San Lorenzo, another Buenos Aires club, for a brief spell which lasted about a year. In 2005, he completed a move to São Caetano of the Campeonato Brasileiro Série A, but never played an official match.
In January 2006, he joined Deportes La Serena on a short term contract. In July 2006, he moved back to Argentina on a short term contract until December with Gimnasia y Esgrima de La Plata. In January 2007, he joined Alianza Lima, only making three appearances before being released. In July 2007, he moved back to Colombia and joined Independiente Santa Fe.
For the 2009 season, he played with Deportes Tolima, with the club having an excellent Apertura campaign as the leaders of the regular season. In 2010, he played with Envigado. In 2011, he moved to Chilean club Unión San Felipe, where he made 55 appearances, and left as the club was relegated in 2012. For the 2013 Finalizacion, Virviescas played for Patriotas Boyaca, and retired shortly after the season ended.