Reece James’ own goal put Villa ahead, but Jorginho quickly levelled from the penalty spot in a clash between two of the many English sides hit by cases of coronavirus.
Lukaku was one of Chelsea’s absentees due to a positive test for draws against Everton and Wolves last week that saw them lose ground in the title race.
But he made his return off the bench at the break and made an almost instant impact to head home Callum Hudson Odoi’s cross.
The Belgian’s blistering run then won a second Chelsea penalty in stoppage time that Jorginho slotted home.
Thomas Tuchel’s men move level on points with Liverpool, who have a game in hand, and back to within six of Manchester City, who were 6-3 winners over Leicester earlier on Boxing Day.
Villa’s own Covid outbreak saw manager Steven Gerrard forced into isolation after he tested positive on Christmas Day.
Gerrard has made a big impression since taking over in November, but this was another lesson in the gap he has to bridge to the Premier League’s top three after defeats to City and Liverpool.
The home side got off to the perfect start when James flicked Matt Targett’s effort over his own goalkeeper Edouard Mendy to open the scoring on 28 minutes.
However, the lead lasted just six minutes due to Matty Cash’s rash challenge on Hudson-Odoi inside the area.
Jorginho was Chelsea’s top league scorer last season despite all of his goals coming from penalties and the Italian international is his side’s leading marksmen in all competitions thanks to nine spot-kicks this season.
Lukaku will expect that to change over the coming weeks as the club’s record signing finds his form after a disrupted start to his second spell at Stamford Bridge.
He is still yet to start in the Premier League since suffering an ankle injury in October, with his positive test for Covid coming just as he was returning to full fitness.
But a Lukaku in form is what Chelsea need if they are to mount a serious title challenge with clashes against Liverpool and City to come in January.
The former Manchester United striker took just 11 minutes to make the difference as he timed his run perfectly to meet Hudson-Odoi’s cross and powered a header low past Emiliano Martinez.
Chelsea should have run out more comfortable winners as Mason Mount dragged his shot wide with the goal gaping after rounding Martinez.
The Argentine then spread himself to deny Hudson-Odoi when one-on-one.
But the only way Ezri Konsa could stop Lukaku as he powered his way through the Villa defence late on was by hauling him down and Jorginho got the better on Martinez once more from the spot.