Castro struck 16 minutes from time as Universitario left Centro Total de Entretenimiento Cachamay in Venezuela with their first win of the campaign after playing out a goalless draw at Cruzeiro last time out.
With time running out, Castro was on hand to poke home the rebound after Mineros goalkeeper Rafael Romo spilled Alejandro Bejarano's shot from distance.
Hosts Mineros finished the match with 10 men following a red card to striker Zamir Valoyes in the 81st minute.
Universitario are two points clear atop the table at the end of matchday two in Group Three after Brazilian Serie A champions Cruzeiro fired blanks again.
Cruzeiro failed to score for the second consecutive Copa Libertadores match, held to a goalless draw by Argentine visitors Huracan at Estadio Governador Magalhaes Pinto in Belo Horizonte.
Paraguayan outfit Libertad notched their first win in Group Seven courtesy of a 1-0 victory at Barcelona.
Jorge Recalde was the hero at Estadio Monumental Isidro Romero Carbo in Ecuador, with his 78th-minute strike from an acute ankle proving to be the match-winner.
Libertad have four points from two games, one more than Estudiantes, who travel to Atletico Nacional on Thursday.
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