The Blues had to do it the hard way as they had to come from behind after Kortney Hause gave Dean Smith’s men a first half lead before second half goals from substitute Christian Pulisic and Olivier Giroud handed Frank Lampard his 15th Premier League win as Chelsea boss from 30 attempts.
Fourth-placed Chelsea are now five points clear of Manchester United in fifth as the race for the Champions League enters its final stretch. The Stamford Bridge outfit are also just three points behind third-placed Leicester City, who they meet in the FA Cup quarterfinals next week.
Chelsea were boosted by the return of Ruben Loftus-Cheek for the first time in 13 months, but the England international failed to stamp his authority on the game, with his replacement, Pulisic pulling Chelsea level five minutes after his introduction.
Both Chelsea goals were assisted by captain Cesar Azpilicueta.
Aston Villa’s failure to hold onto their lead means their battle to beat the drop continues as they remain in 19th position, one point adrift 17th placed West Ham United.
Villa are back in action on Wednesday when they travel to Saint James’ Park to take on Newcastle United while Chelsea host champions Manchester City a day later.