Ruben Loftus-Cheek’s first Premier League goal and a penalty from Alexandre Pato on his long-awaited debut gave Chelsea a commanding lead at half-time.
After a subdued opening 20 minutes, in which Chelsea were content to control possession, the visitors broke through at the end of a fine passing move.
John Obi Mikel started it by upping the tempo, Pedro spread the ball wide for Cesar Azpilicueta and the Spaniard’s cross was turned in by Loftus-Cheek, via a deflection off Joleon Lescott.
Pato, brought in in January on loan from Corinthians, had come on shortly before the first goal after Loic Remy went off injured.
And he got his first goal from the spot in injury time, after being flattened by a falling Aly Cissokho in the box.
Pedro had had Chelsea’s first chance of note, with a right-efforted that just cleared the angle of post and bar.
Rock-bottom Villa were not cowed by the Blues, though, and Rudy Gestede and Carles Gil both forced Thibaut Courtois into saves.
Jordan Ayew, the hosts’ stand-out player in the first half, then rolled a shot just wide of the post, while Loftus-Cheek did the same at the other end after robbing Idrissa Gueye.
As well as Pato, Chelsea gave a debut to January signing Matt Miazga as part of a reshuffled back four, with John Terry and Gary Cahill both out.
Subs: Bunn, Okore, Bacuna, Lyden, Veretout, Grealish, Sinclair.
Chelsea: Courtois; Azpilicueta, Ivanovic, Miazga, Baba; Mikel, Fabregas; Pedro, Loftus-Cheek, Kenedy; Remy.
Subs: Begovic, Clarke-Salter, Matic, Oscar, Traore, Pato, Falcao.