Banfield believed that the referee had awarded an indirect free kick on the edge of the area in the 36th minute, and goalkeeper Cristian Lucchetti remained rooted to the spot as Matias Abelairas (pictured) floated the ball over the wall and into the net.
Amid furious Banfield protests, the referee allowed the goal to stand.
Colombian striker Radamel Falcao Garcia added River's second in the 83rd minute from a chance set up by new signing Cristian Fabbiani who, weighing close to 100 kgs, has already become a cult figure at the club.
The win left River with seven points from three games in the Clausura championship, level with Newell's Old Boy's, Colon and Godoy Cruz.
Titleholders Boca Juniors lost for the second week in a row when they were beaten 1-0 at Lanus, Argentina under-20 international Eduardo Salvio scoring the only goal after three minutes.
Both coaches -- Luis Zubeldia of Lanus and Carlos Ischia of Boca -- were sent off in the last 10 minutes.
First-half goals from Christian Cellay and Jonathan Santana gave Estudiantes their first win as they beat San Lorenzo 2-1 despite missing captain Juan Sebastian Veron, who was rested for the Libertadores Cup.
Gonzalo Bergessio pulled one back in the 81st minute.
