Marcelo Gallardo's men were held to a 1-1 draw at home to second-bottom Olimpo, marking a third straight game without a win.
Racing Club's victory saw River Plate's advantage at the top reduced to one point.
River were on track for a win when Ramiro Funes Mori headed in a Leonardo Pisculichi corner in the 24th minute.
But ordinary defending allowed Olimpo to level in the 70th minute as Miguel Borja fired an effort into the bottom corner from 20 yards.
Racing Club took on the league's bottom side in Quilmes, and they made no mistake to record a 1-0 win.
Gustavo Bou's 30-yard free-kick went through the defensive wall and into the top corner.
Both teams had already been reduced to 10 men, with Racing's Yonathan Cabral and Quilmes' Alan Alegre seeing red in the second half.
Independiente moved into third courtesy of a 4-1 thrashing of Lanus, who slipped to fourth.
Lanus led in the second minute thanks to Silvio Romero, but goals from Sebastian Penco and Daniel Montenegro had Independiente ahead before half time.
Red cards to Facundo Monteseirin and Maximiliano Velazquez ended Lanus' hopes of a comeback, and the hosts sealed their win through goals to Juan Martin Lucero and Victor Cuesta.
Defensa y Justicia edged Atletico Rafaela 2-1 and San Lorenzo were convincing 4-0 winners over Belgrano.
Rosario Central and Velez Sarsfield played out a 0-0 draw, while Gimnasia La Plata drew 1-1 with Banfield.
Godoy Cruz and Estudiantes were unable to be separated in a 1-1 draw and Arsenal held Boca Juniors to a 1-1 draw.
Maxi Rodriguez was on the scoresheet in Newell's Old Boys' 2-1 win at Tigre.
