He made his first-team and Primera División debut in a 1–0 win against Estudiantes de La Plata on 17 September 2006, taking the pitch in the 85th minute.
After six Liga I and two Champions League appearances he was recalled by Porto but,[11] in the following transfer window, moved to Club Deportivo Universidad Católica in Chile as a replacement for Al Ain FC-bound Milovan Mirošević, being officially presented on 25 January after agreeing to a six-month loan.
[12][13] Costa made his official debut against Unión La Calera in a 2–1 Primera División defeat at the Estadio Municipal Nicolás Chahuán Nazar on 12 February 2011, starting the match as right back and being replaced by Santiago Dittborn.
[15][16] On 23 April 2011, Costa netted his first league goal for Universidad Católica after a notable free kick against Cobresal in a 5–3 win;[17] his solid performances overall made him a regular starter in the Juan Antonio Pizzi-led side, which qualified to the 2011 Copa Sudamericana.
In the national championship playoffs finals against Club Universidad de Chile, he scored in the first leg in a 2–0 home victory[18] but was sent off in the decider (4–1 loss).