The home side's early pressure paid off as they took the lead through a James own goal on 28 minutes.
Thomas Tuchel's side are looking to keep up the heat on Premier League leaders Manchester City after dropping behind Pep Guardiola's side in the title race.
On top of that, they have been scoring goals consistently at home almost for the whole of 2021.
Lukaku's involvement proved to be the difference, putting his side into the lead with a glancing header into the far bottom corner following a floated cross from Hudson-Odoi.
With Leicester and Liverpool also winning at the time, Chelsea were already fifth by the time Anwar El Ghazi converted a penalty to make it 2-0 after Traore had been tripped by Jorginho 52.
John McGinn went close, winning the ball high up the pitch and curling just wide from 20 yards, and while Chelsea had good news from their London rivals Tottenham equalising at Leicester to move them fourth, Villa soon went ahead via a familiar face.