Striker Facundo Parra scored twice for the home side in the biggest game of the first division since the relegation last year of River Plate whose derby with Boca Juniors is the Argentine 'Superclasico'.
Racing had teenage midfielder Bruno Zuculini and Colombia striker Teo Gutierrez sent off between the 58th and 69th minutes.
It was Gutierrez's second red card in the championship.
Basile's side took the lead following a defensive blunder by home captain Gabriel Milito midway through the first half.
Striker Gabriel Hauche latched on to the former Barcelona centre-back's poor clearance on the right wing, raced into the box and passed square to Gutierrez who tapped the ball in.
"It was my terrible mistake that allowed Racing to go ahead but it was their only clear chance. We played better and deserved the win," Milito told Futbol Para Todos.
Racing's holding midfielder Agustin Pelletieri cleared an Independiente chance off the line two minutes into the second half as the home side continued to take the game to their opponents.
Ten minutes later referee Sergio Pezzotta controversially ruled Zuculini had pushed Independiente's Patricio Rodriguez, awarding a penalty.
