The visitors enjoyed most of the early possession and went close to an opener when a corner was half-cleared to Pedro, who turned past one challenge before curling an 18-yard effort just wide of the target.
The Blues eventually broke the deadlock in the 26th minute and it was a first Premier League goal for Ruben Loftus-Cheek. Cesar Azpilicueta crossed from the right and the young Englishman turned it goalwards, although the ball was helped past Brad Guzan via a deflection off Joleon Lescott.
Villa, playing their first match since Remi Garde's departure earlier this week, came close to an equaliser five minutes later as first Carles Gil's shot was palmed out by Thibaut Courtois before Baba Rahman's clearance hit the onrushing Jordan Ayew, with Courtois alert to make another save.
Rahman and Ayew went close at either end before Chelsea doubled their lead on the stroke of half time. Alexandre Pato, who came off the bench to replace Loic Remy and make his long-awaited Blues debut, was brought down in the box by Aly Cissokho and stepped up to slam home the penalty and mark his Chelsea appearance with a goal.
It was three less than a minute after the resumption as Brazilian substitutes Oscar and Pato combined to set up Pedro, who rolled home from eight yards.
The Spaniard made it four shortly after, this time squeezing home from a tight angle after Guzan failed to hold Pato's curling shot.
Rahman was closest to a Chelsea fifth goal, while it went from bad to worse for Villa when Alan Hutton was sent off for a second yellow card late on.