Goals either side of half-time from midfielder Cesar Mansanelli and striker Cesar Pereyra gave the second-tier Nacional B side the victory that put them on the verge of a place in the top flight.
River, whose last title was in the second half of the 2007/08 season, find themselves in the dire situation as a result of their poor three-season points average that determines relegation in Argentina.
The match was interrupted for 20 minutes after River went two goals behind early in the second half. Some of their fans broke a hole in the perimeter fence and stormed onto the pitch in the city of Cordoba.
The fans remonstrated with their own team's players, demanding more effort from them, before being ejected and order was gradually restored.
Belgrano went ahead with a penalty converted by Mansanelli midway through the first half after defender Adalberto Roman handled at a corner.
They added the second five minutes into the second half when defender Luciano Lollo glanced Mansanelli's corner towards the far post where Pereyra turned it past goalkeeper Juan Pablo Carrizo into the net.
THREE SUSPENDED
Belgrano midfielder Franco Vazquez had a chance to bury River near the end when defender Jonatan Maidana slipped and lost possession but he hurried his shot over from the edge of the box.
River had dropped experienced strikers Mariano Pavone and Leandro Caruso in favour of youth, and while 37-year-old Matias Almeyda gave his all in the midfield holding position his lack of pace was often exposed.
River had several chances from free-kicks, corners and long range shots but Belgrano goalkeeper Juan Carlos Olave was equal to them all, highlighted by a superb stop from Carlos Arano's drive.
They lost their shape, and their discipline, as the match wore. Captain Almeyda, Roman and defender Paulo Ferrari were booked and will miss the second leg through suspension having accumulated five yellow cards.
River need to get back on level terms in the return leg at the Monumental on Sunday and will survive with an aggregate draw as the result favours first division sides.
Earlier on Wednesday, Gimnasia beat nine-man Huracan 2-0 in a one-off match at the Bombonera to qualify for the other play-off, while condemning the losers to relegation.
