Philippe Coutinho silenced the Elland Road crowd with a 22nd-minute opener for Aston Villa.
Leeds came out fighting in the second half but their attacking efforts came to nothing.
The visitors cut open the Whites' defence for Matty Cash to easily double Villa's lead.
Calum Chambers scooped a lovely effort into Illan Meslier's top corner to seal a victory for the Birmingham side and confine Leeds to another disappointing result.
The visitors cut open the Whites' defence for Matty Cash to easily double Villa's lead.