Lucas Melano opened the scoring in the 39th minute at the Estadio Juan Domingo Peron after a scramble in the area.
From a corner kick, Paolo Goltz headed the ball, Racing keeper Sebastian Saja blocked it, Carlos Izquierdoz shot towards the post and Melano sent it into the back of the net.
Seconds before the break, Santiago Silva started a counter-attack and passed the ball to Silvio Romero, who took on a defender and beat Saja with a right-footed strike.
Racing pressed forward and reduced the deficit 19 minutes into the second period, when Valentin Viola headed the ball into the top-left corner.
Lanus midfielder Diego Gonzalez told Fox Sports: "We had to do a lot of running. Racing have very talented players in midfield and going forward.
"The lead gives us confidence, as does winning away from home, but we still have to play another match."
Racing's debutant forward Roger Martinez, meanwhile, was unable to hide his disappointment.
"I had the chance to play my very first match at Racing, but I missed some chances," he said.
"We must keep working hard in order to correct mistakes. Anything is possible."