Teenage striker Cristian Pavon broke the deadlock in the 84th minute, tucking a shot from the left between goalkeeper Marcelo Barovero and the post.
Two minutes later, fellow substitute Pablo Perez made sure of the victory when he scored from the rebound after Barovero had parried midfielder Nicolas Lodeiro's effort.
"That's the loveliest thing that's happened to me since I got to Boca," the 19-year-old Pavon told Futbol Para Todos, while Boca coach Rodolfo Arruabarrena praised the teenager's initiative.
"Cristian's goal came from the opposite wing to which I’d asked him to play, that's the player's intelligence," he told reporters.
Boca have 27 points from 11 matches, three points more than River and San Lorenzo, who beat Velez Sarsfield 1-0 on Saturday.
Belgrano had the chance to go second but were held 1-1 at Union in Santa Fe and remain fourth with 23 points.
Sunday's "superclasico" league clash was an hors d'oeuvre to the meeting of the bitter rivals in the last 16 of the South American Libertadores Cup, which begins with the first leg at River on Thursday.
River had their chances too and striker Rodrigo Mora forced goalkeeper Agustin Orion into a reflex save to tip over his looping volley from the right edge of the box early in the second half.
Mora also hit the angle of post and bar with another effort from the left on the hour mark as River took the game to Boca after the interval.
The match began with Boca pushing River into their own half and forcing the visitors to play on the counter-attack, not their preferred game.
Boca's Dani Osvaldo hit the bar with a volley in the 10th minute and fellow striker Andres Chavez narrowly missed the target on the half hour after the Italy striker stepped over Federico Carizzo's right cross.
At that point River coach Marcelo Gallardo could be heard screaming at his players: "Lets play a bit!"
Two minutes later, River almost took the lead with their best move of the first half when winger Carlos Sanchez met striker Teo Gutierrez's square pass with the outside of his right foot only to see the ball come back off the bar.
"In three minutes we lost a match we had under control ... They hadn't been creating danger," Gallardo added.
(Editing by Nick Mulvenney)
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