Thomas Tuchel's side had picked up one win in their previous four Premier League matches, but Chelsea turned things around on Sunday as they came from behind to claim an important victory over Villa.
Defender Reece James scored an own goal to hand Villa the lead midway through the first half, but Chelsea midfielder Jorginho levelled the scores from the penalty spot shortly after. Lukaku came off the bench at half-time and made his presence known, nodding home on 56 minutes. Jorginho scored another penalty in stoppage time after Lukaku was brought down in the box.
Villa enjoyed the better of the chances in the opening stages, with striker Ollie Watkins racing down the left wing and into the 18-yard box on multiple occasions but he could not take advantage.
The home side's early pressure paid off as they took the lead through a James own goal on 28 minutes. Villa defender Matt Targett delivered a cross, but it deflected off James' head and past Chelsea goalkeeper Edouard Mendy.
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.
Lukaku raced behind Villa's back line in stoppage time before winning Chelsea's second penalty of the match when he was brought down by Ezri Konsa, allowing Jorginho dispatch home.
"I needed a performance like this," said Lukaku, "It's been difficult getting [on at] the end of games. I kept working hard. I'm happy with my performance and have to push on," he added.
The former Manchester United and Inter Milan striker said Chelsea remained in the race to catch leaders City.
"We are the hunters now. The last results were not the best and now we have to chase. We have to treat every game like a final. Today we won and now we have to push on," he said.