Osvaldo, on loan from Premier League side Southampton, struck in the 43rd minute as Boca made it two wins from as many Group Five games.
Diego Riolfo had cancelled out Juan Komar's opening goal before Osvaldo got on the scoresheet at the Estadio Alberto Jose Armando in Buenos Aires.
Boca top the group with six points, while Uruguay's Wanderers (three points) are second – ahead of Palestino and Zamora.
Komar headed Boca into a 33rd-minute lead on Thursday, getting on the end of Nicolas Lodeiro's set-piece from the right.
Wanderers were level straight from the restart.
Gaston Rodriguez played in Riolfo, who fired past Agustin Orion at his near post.
But Osvaldo put Boca ahead two minutes before half-time, getting on the end of a Nicolas Colazo cross to head in.
In the group's other game, Alejandro Marquez's goal saw Palestino to a 1-0 victory at Zamora.
Internacional claimed their first win in Group Four, beating Universidad Chile 3-1.
Goals from Andres D'Alessandro, Jorge Henrique and Eduardo Sasha saw the Brazilians clinch their first points in the group.
D'Alessandro put his side ahead on the stroke of half-time, blasting a penalty into the top corner.
Henrique doubled their lead with a neat finish in a one-on-one just after the hour-mark before Gustavo Canales' good finish dragged Universidad back into it.
Sasha put away Charles Aranguiz's cross in the 78th minute to ensure Internacional would take all three points.
Internacional are second to Emelec in Group Four.
Santa Fe hold a perfect record in Group One after Wilson Morelo's hat-trick saw them to a 3-1 win over Colo Colo.
