River missed an 87th minute penalty when Rogelio Funes Mori fired his effort high and wide of the goal and Belgrano goalkeeper Juan Carlos Olave was sent for his celebration in which he appeared to make gestures at the referee.
The referee was surrounded by protesting Belgrano players and the visitors, who had already made three substitutions, ended the game with centre forward Juan Martin in goal.
River, one of the country's biggest clubs, were given a rapturous reception on a foggy evening but left the pitch amid jeers and insults.
Their problems began two minutes before halftime in Sunday's match when goalkeeper Daniel Vega failed to hold a cross and Lucas Melano headed the visitors in front.
Manuel Lanzini pulled one back with 15 minutes left before River were awarded a hugely controversial penalty which Funes Mori blasted over.
River were relegated just over one year ago to Belgrano in a two-leg play-off.
River's arch-rivals Boca Juniors had an even worse start to the 2012/13 title race as they lost 3-0 to Quilmes on Saturday while defending champions Arsenal began with a 1-0 win over Union.
The championship this season is being played under a new format, with the contest divided into two halves and the winners of each meeting in an end-of-season final. Previously, two separate championships were held in the Argentine season.