Diego Tardelli scored the only goal of the game in Argentina, as the Brazilian visitors triumphed at the Estadio Ciudad de Lanus.
In the 67th minute, Lanus were unable to clear a long throw and Mineiro gained possession in their forward third, before Brazil striker Jo linked with Guilherme, who teed up Tardelli on the left-hand side of the box to score.
The Recopa Sudamericana pits the reigning champions of the Copa Libertadores and the Copa Sudamericana against each other.
The 2013 Libertadores champions - Mineiro - will be favourites to win the 2014 Recopa Sudamericana as they will start the second leg in Belo Horizonte - where they have lost just once in their past 15 games in all competitions - with a one-goal advantage.
The second leg will be held on July 23.
