Vega left home to attend the Centro Andaluz de Teatro, a prominent acting school near Seville. After two years of studying acting, and another two studying journalism, Vega moved to Madrid to pursue her dream. She spent much of her time auditioning and working at a bar before appearing in three episodes of the Spanish series "Menudo es mi Padre" (1997). She soon found consistent work playing Olga on the sitcom "Más Que Amigos" (1997), but was lost in the shuffle on her next project, the ensemble series "Compañeros" (1998).
Paz was immediately successful. She became a regular on the TV series Más que amigos in 1997, then moved into film work and went on to win several awards for her starring role in Lucía y el sexo/Sex and Lucia (2002). She also received an Audience Award nomination at the European Film Awards for the title role in Carmen (2003).