Former Boca player Maidana rose above the defence to glance a corner from the right by Erik Lamela past diving goalkeeper Javier Garcia and inside the far post in the 54th minute.
It was River's first win over Boca in six league matches since 2007. In 187 league meetings, Boca have won 68 and River 62.
"This was a final and they played it like that, with the 'sacred fire'," River's caretaker coach JJ Lopez told reporters.
Right-back Paulo Ferrari, speaking of Lopez and his staff, said: "They are people of the club who told us what it takes to play matches like this."
Garcia made diving saves from Walter Acevedo's rasping free-kick from outside the box and Ariel Ortega's shot from the right 10 metres out at the end of a move that began on the left.
Both sides, the giants of Argentine football, have had a dismal season languishing in the bottom half of the standings, though River's victory, their first in eight matches, lifted them into eighth place with 21 points. Boca are in 15th on 17 points.
It was River's first match under Lopez, one of the club's most distinguished former midfielders who helped them win several titles in the 1970s, after the sacking last week of coach Angel Cappa.
Rumours abounded over the last few days that Boca coach Claudio Borghi would resign if his team lost the "superclasico".
