Fernando Torres headed the home side in front in the third minute and goals from David Luiz and Branislav Ivanovic effectively decided the contest before the break.
Frank Lampard then marked his 500th Premier League start with a trademark long-range effort that took him ahead of Bobby Tambling's record of 129 top-flight goals for Chelsea, before Oscar, Eden Hazard and a Ramires double completed the rout.
Although this was the ninth game of Rafael Benitez's Chelsea reign, these were the first Premier League goals scored under him at Stamford Bridge and this performance will surely encourage fans that his teams can entertain.
Benitez certainly seems to bring the best out of Torres. The Spanish forward was quick off the mark to steal a yard on Ciaran Clark and connected beautifully with Cesar Azpilicueta's right-wing cross to beat Brad Guzan and score his seventh goal in six games.
Luiz, playing in midfield, then doubled the lead just before the half-hour mark with a fizzing free-kick that beat the wall and was far too fast for Guzan.
Villa's young side were struggling to deal with the movement and flair of Chelsea's forwards and the goalkeeper was left exposed again five minutes later.
Guzan saved well from Gary Cahill initially but Ivanovic was there to head in the rebound with the visitors' defence flatfooted.
The American goalkeeper had a busy afternoon and made a series of fine saves, denying Juan Mata and Victor Moses early in the second half.
But there was nothing he could do to stop Lampard's superb strike from distance that capped a landmark game for the 34-year-old who later departed to a standing ovation.
The three Chelsea substitutes then took over. Premier League debutant Lucas Piazon found Ramires to blast in the fifth before Oscar scored from the spot after being pulled down by Chris Herd.
Hazard then scored a brilliant solo effort cutting in from the left channel and Chelsea had the chance to make it eight when referee Phil Dowd awarded a second penalty but Piazon saw his shot saved.
But the Blues were not to be denied and Ramires sidefooted home just before the end to complete Villa's heaviest ever Premier League defeat and crown a memorable day for Chelsea, Benitez and their talismanic midfielder Lampard.