Villa's formidable home form this season made them firm favourites to reach the last 16 but Chelsea produced a devastating attacking display to ease the pressure on manager Mauricio Pochettino.
Pochettino's short tenure at Stamford Bridge was under severe scrutiny after the 4-2 home defeat by Wolverhampton Wanderers on Sunday left them languishing in 11th place in the Premier League.
Chelsea's cup performances are rescuing their season, already reaching the Carabao Cup final against Liverpool at Wembley on 25 February, while this was surely their best performance of the campaign against a Villa side who have lost only two games out of 16 on home territory.
Villa's hopes of a comeback were extinguished nine minutes after the interval when Enzo Fernandez curled a magnificent 25-yard free-kick into the top corner, tantalisingly away from the reach of Villa goalkeeper and fellow Argentina World Cup winner Emiliano Martinez.
Substitute Moussa Diaby pulled one back for Villa in stoppage time but it could not even be considered consolation for the home side and Chelsea now face Leeds United at Stamford Bridge in the fifth round.
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