In the first half Chelsea's free-roaming wingers Damien Duff and Arjen Robben created most of the chances, switching from side to side to baffle their markers.
Robben's fourth-minute cross handed Thomas Sorensen his first headache of the afternoon, but the ball just failed to reach centre-forward Eidur Gudjohnsen.
For Villa, Ulises De la Cruz sent over a cross in the seventh-minute which just evaded Juan Pablo Angel's head, while Lee Hendrie had three attempts from distance.
Villa didn't let Chelsea settle on the ball, continuously snapping at their heels and denying them thinking space.
On the half-hour mark Chelsea finally got the breakthrough, predictably through Duff who makes a habit of scoring the first goal at Stamford Bridge.
After being fed the ball by Robben, Duff steamed down the right wing, before switching the ball to his right foot and sending a superb shot beyond Sorensen.
Mark Delaney prevented Villa from going two down in the 37th minute when he cleared Robben's shot of the line, before Villa had their best chance of the half when Peter Whittingham's free-kick needed a desperate lunge by Petr Cech to keep it out.
In the second half, Villa were restricted to long-range efforts while Chelsea seemed content to sit on the lead and conserve their resources with tricky away fixtures looming at Portsmouth and Liverpool.
In the end it was a routine, rather lacklustre win in front of a quiet crowd who are now so accustomed to comfortable victories that they spend their time devising ironic chants.