Substitute forward Sebastian Palacios scored two second half goals to secure the victory after Argentina World Cup midfielder Fernando Gago had put Boca ahead with a 29th-minute penalty.
"I thought we played well overall even if we were too hurried up front in the first half and lost concentration (for their equaliser) before halftime," Gago told reporters.
Boca were awarded the penalty when defender Ivan Furios held Daniel Diaz in a firm grip around his arms and waist at a free kick having been warned for taking hold of the centre back at a previous set piece in the Olimpo box.
Olimpo equalised when midfielder Jonathan Blanco was left unmarked at a corner and beat goalkeeper Agustin Orion with a sharp header into the roof of the net one minute before the interval.
The outstanding Gago might have scored again five minutes into the second half but goalkeeper Nereo Champagne uncorked a brilliant reflex save to tip the Boca playmaker's shot over the bar.
Olimpo almost went in front in the 62nd minute when Juan Cobo looked set to score from a corner but Orion scrambled across goal to save.
Palacios came on right after Olimpo's missed chance and 11 minutes later volleyed Boca in front after latching on to a poor clearance by Champagne.
The stocky striker made sure of the result when he tapped home winger Federico Carrizo's low left cross in the 86th minute.
Argentine-born Italy striker Osvaldo signed for Boca on Thursday on loan from Southampton having quit Inter Milan after being disciplined by coach Roberto Mancini.
He could make his debut for the team he supported as a boy in the Libertadores Cup Group Five opener away to Chile's Palestino on Wednesday.
Boca's arch-rivals River Plate were away to promoted Sarmiento in Junin later on Sunday (12:30 a.m. Monday).
(Reporting by Rex Gowar, editing by Nick Mulvenney)
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