Villa's only serious first-half threat came after 33 minutes, when referee Mark Halsey awarded a contentious free-kick when Emile Heskey tumbled under the tamest of challenges from John Obi Mikel.
Young curled a 20-yard effort against the bar, and Heskey headed the rebound wide when he should have scored.
Terry was again thwarted from a Lampard corner three minutes after the interval, when Petrov cleared his header off the line.
It was the signal for Villa to finally show some of the power and pace that elevated them to third place in the Premier League before kick-off.
Gabriel Agbonlahor tested Petr Cech after muscling Alex aside, and the keeper also saved well from Gareth Barry as Villa started to exert some concerted pressure.
O'Neill backs 'leggy' Villa to bounce back
Chelsea rediscovered their attacking instincts as Villa pressed for the equaliser, with Drogba shooting off target from a tight angle and Friedel saving well from Jose Bosingwa after he was played in by the striker.
Substitute Deco showed sublime skill to set up Michael Ballack in stoppage time, but Friedel was equal to the task and turned his rising drive over the top.
Villa were unable to mount a response and the importance of Chelsea's victory was emphasised by the celebrations at the final whistle.
Aston Villa: Friedel, Cuellar, Davies (Carew 70), Knight, Luke Young, Milner, Petrov, Barry, Ashley Young, Heskey, Agbonlahor.
Subs Not Used: Guzan, Sidwell, Delfouneso, Salifou, Shorey, Gardner.
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