Leonardo Ponzio took less than two minutes to make the breakthrough for River, who were facing their fierce rivals for the first time since returning to the top flight.
And the hosts looked well on course for all three points when Rodrigo Mora doubled their advantage in the 70th minute, much to the delight of the vast majority of the 50,000 sell-out crowd at El Monumental.
However, Santiago Silva pulled a goal back from the penalty spot in the 76th minute and then Walter Erviti snatched a last-gasp equaliser to stun the hosts.
The result did little for either team's cause, though. Julio Falcioni's Boca finished the weekend in sixth place in the Apertura standings - seven points behind leaders Newell's Old Boys - with Matias Almeyda's River three points and three positions worse off.
Elsewhere on Sunday, Belgrano Cordoba climbed to third spot courtesy of a 1-0 home triumph over bottom club Union Santa Fe.
Substitute Cesar Pereyra netted the game's only goal midway through the second half - shortly after the visitors had had defender Bruno Bianchi sent off.
Lanus were also 1-0 winners, Mario Regueiro's 58th-minute strike enough to sink Argentinos Juniors and lift the victors to fifth.