River, record 33 times league champions and never relegated, will meet Nacional B (second division) side Belgrano over two legs in the relegation-promotion play-offs after substitute Leandro Diaz scored a stoppage-time winner at a packed Monumental.
Striker Silvio Romero put Lanus, who finished the Clausura championship second to champions Velez Sarsfield, ahead on the half hour with a low shot into the bottom corner from the edge of the box.
River equalised two minutes after half-time when teenage midfielder Erik Lamela turned in right-back Paulo Ferrari's cross, sparking a frenetic series of attacks by the home team.
Lamela and striker Leandro Caruso missed chances to win the match for River before Diaz's sucker punch, a superb shot inside the far post beyond diving Argentina goalkeeper Juan Pablo Carrizo.
Huracan, beaten 5-1 by Independiente, and Gimnasia finished with the same three-season points averages and must meet to decide which team is relegated and which faces a Nacional B side in a play-off.
Gimnasia, who had gone two goals up, were held 2-2 at home in La Plata by Boca Juniors after conceding a late equaliser by defender Cristian Cellay from a header by Martin Palermo in the striker's last match before retiring.
Quilmes, who lost 1-0 at home to Olimpo, were relegated.
River will meet Belgrano away in Cordoba on Wednesday with the return in Buenos Aires the following Sunday.
Relegation is decided on points averages over three seasons, with River paying for their poor results in 2008/09 and for taking only four points from their last seven matches in the Clausura.
