The Blues faded after a wonderful start to the game and dropped two precious points by playing some tetchy, lacklustre football late on as a difficult festive period for the West Londoners continues.
On that note, let's have a look at a few Twitter reactions after the game.
Oliver Giroud opens the scoring for Chelsea
In-form Olivier Giroud rounded off a wonderful Chelsea move by tucking away a header to the corner of the goal. The Blues dominated the rest of the half and appeared full of intent, with Christian Pulisic coming close twice.
The USA international, who set the field ablaze alongside Callum Hudson-Odoi on either flank, should have doubled his team's lead. After Mason Mount missed the roof of the net from close range as well, Chelsea went into the tunnel with their tails up.
However, Villa came out determined and hit back with an equaliser through Anwar El Ghazi. Matty Cash produced a beautiful cross towards the goal-scorer, who was left unmarked at the far post.
In the build-up to the goal, Jack Grealish's apparent foul on Andreas Christensen sparked debate, with fans and pundits suggesting that there should have been a VAR check.
John McGinn's rocket from distance rattled the Chelsea woodwork while Hudson-Odoi and Pulisic tested Emiliano Martinez in an action-filled finale.
However, Chelsea will consider this as an opportunity lost while Villa continue to surprise the fraternity with their tenacity and gritty displays. The Blues have now won only one of their last five Premier League matches.