Marcelo Gallardo's River were beaten 1-0 at home to Estudiantes on Wednesday.
Diego Vera's sixth-minute goal was all that separated the two teams at the Estadio Monumental Antonio Vespucio Liberti.
Vera made a driving run into the penalty area and reacted quickest as River goalkeeper Marcelo Barovero spilt the ball out of his hands.
Estudiantes ended the match with 10 men after midfielder Sebastian Prediger saw red for a second bookable offence in injury time.
River remain two points clear at the summit with 32 points from 15 matches after Lanus lost 3-0 at Tigre on the same day.
Lanus were on a 10-match unbeaten league run prior to kick-off, but the visitors fell away in the second half as they conceded three goals.
Tigre striker Leandro Garate broke the deadlock in the 61st minute and the dismissal of Lanus substitute Maximiliano Velazquez four minutes later led to two more goals.
Both Gabriel Penalba and Lucas Wilchez came off the bench to seal all three points for Tigre, who snapped a four-match winless streak.
Meanwhile, fourth-placed Independiente earned a 1-1 draw from their trip to Arsenal on Thursday.
