Former Manchester United and England captain Rooney converted a second-half penalty, while Acosta scored a brace to snap Atlanta's seven-match unbeaten streak on Monday (AEST).
Atlanta had the chance to return to the top of the east after Supporters' Shield leaders New York Red Bulls were stunned by Montreal Impact on Saturday but Gerardo Martino's high-flying side were no match for DC.
DC – needing all three points to stay in the play-off picture – opened the scoring in the 29th minute when Rooney flicked on a header and Acosta latched on to the ball before side-stepping opponents and firing a low shot past Brad Guzan.
Atlanta, though, responded 10 minutes later via Jeff Larentowicz, who headed home a powerful equaliser to ensure the scores were level at half-time.
Rooney restored DC's lead seven minutes into the second half with a successful penalty after Paul Arriola was fouled by Ezequiel Barco.
And Acosta sealed the points with 14 minutes remaining after another mazing run into the penalty area.
The result ended back-to-back defeats for DC – who moved within six points of the play-off spots in the east – while Atlanta remains a point behind the Red Bulls.