Basile at a loss to explain poor Racing form
Banfield, who came into the game on a run of six successive defeats, were a man down for an hour after defender Marcelo Bustamente was sent off and conceded a penalty converted by striker Teofilo Gutierrez in the third minute.
Banfield equalised in the 11th minute when their goalkeeper Cristian Lucchetti had a penalty saved by his opposite number Sebastian Saja but Andres Chavez netted the rebound.
Banfield's winner, which leaves Racing with one point from three matches, came in added-time from striker Rodrigo Lopez's header at a free-kick.
"My teams go out to attack, I was hired to play like that," Basile told reporters. "We dominated but didn't create chances. We have a good team but [the opposition] always scores. I want to win, up to now I haven't found the formula."
With 11 minutes to go, Gutierrez earned a second booking and was sent off when he kicked the ball out of Lucchetti's hands as the goalkeeper was looking to throw the ball to a team-mate.
Gutierrez was booed off the Cilindro pitch by Racing's fans, who also had harsh words for Basile at the end. The 68-year-old coach retaliated angrily: "Who are you insulting? I'll fight you all."
In other matches, title holders Boca Juniors beat Newell's Old Boys 2-0 at the Bombonera to extend their unbeaten league run to 32 matches and share top place on seven points from three games with Velez Sarsfield, Tigre and All Boys.
Boca continued to lean on a stingy defence that has conceded only six goals in their last 22 league matches while scoring through striker Dario Cvitanich and a brilliant Juan Roman Riquelme free-kick.
Racing's arch-rivals Independiente are even worse off than their neighbours and languish in bottom place after three defeats, their latest 2-0 to Estudiantes in La Plata on Saturday.
San Lorenzo, another of the struggling big clubs, had a happier weekend with a 1-0 win at Argentinos Juniors.