Lukaku was on the end of a neat team move to stroke the Red Devils level from close range seven minutes after Willian fired the visitors ahead just after the half-hour mark.
He then provided a pin-point cross which substitute Jesse Lingard headed home on 75 minutes to send United back up to second in the Premier League and six points ahead of their London rivals.
Three points a merit of hard work
"Not really" was how Lukaku responded when asked if doubts over his performances against the top flight's biggest sides affect him ahead of more significant meetings like those of this weekend.
Despite the 24-year-old's recent struggles in matches against the other representatives of the Premier League's top six, he insisted he "always works hard" and three points against his former club "is great."
Before his terrific showing against Antonio Conte's side, Lukaku hadn't contributed to a single goal in six previous league meetings against United's five rivals since his £75m July move from Everton.
Satisfaction comes with improvement
United started slowly and were on the back foot to the point where Chelsea's lead was deserved, and the Belgian stressed that the team "had to work really hard" and "were well prepared" for the test.
Amidst all of the focus on his record against the best teams, the Red Devils' no. 9 simply put that he "just wants to work hard for the team" and when improvement shows, he can then be "really satisfied."