River joined Velez Sarsfield, who beat title holders Argentinos Juniors 2-0 at home on Saturday, at the top of the Argentine Apertura championship standings as the only teams with maximum points after three matches.
Coach Angel Cappa's River side, much improved from last season, took the lead in the ninth minute with their first chance by striker Rogelio Funes Mori who turned in a mishit shot by defender Jonatan Maidana.
Striker Andres Silvera equalised in the 18th minute with a low shot from the left past the diving Juan Pablo Carrizo.
River were ahead again within a minute when teenage midfielder Manuel Lanzini, standing in for suspended veteran Ariel Ortega, laced a superb ball through to Funes Mori who scored his second.
River's right-back Paulo Ferrari then increased their lead in the 25th minute from Diego Buonanotte's pass with a shot that keeper Adrian Gabbarini touched but could not keep out.
Cappa praised veteran holding midfielder Matias Almeyda for the "huge job he is doing" and said River, who need to boost their low three-season points average to stave off relegation, "must always be thinking of winning the championship".
Independiente almost stole a point at the death when a shot by midfielder Federico Mancuello hit the post and bounced off Carrizo into the goal, before the keeper made a fine diving save from a Silvera shot heading for his top left corner in stoppage time to ensure River won.
Boca, without playmaker Juan Roman Riquelme who is recovering from knee surgery, lost for the second successive game after All Boys scored twice in the first half with a Mauro Matos penalty and an Eduardo Dominguez header.
Of the three other teams that were equal with River and Velez on six points after two matches, Banfield and Estudiantes drew 0-0 while Racing Club were beaten 2-1 by San Lorenzo.
