Substitute Jesus Navas looked to have given the visitors the advantage with a 76th-minute counter-attack goal to cancel out Ramiro Funes Mori's opener on the stroke of half-time.
However, Lukaku rose to power home a perfect Gareth Barry cross less than two minutes later for his 12th goal in as many matches to swing the momentum back in his side's favour - but only just.
The sight of him limping off late on was an initial concern but manager Roberto Martinez played down the injury scare, although the Belgium international is unlikely to be risked in Saturday's FA Cup tie at home to Dagenham and Redbridge.
"Romelu had a knock on his ankle
We are going to assess him
I don't know if he will be available for the weekend but I don't think it is too serious," said Martinez, who has greater worries over midfielder Tom Cleverley and right-back Seamus Coleman.
"Tom and Seamus are very similar, Seamus with his calf is probably the most serious, those things are between three to four weeks."
Everton withstood City's early huffing and puffing without much threat and eventually seized control of midfield with Mo Besic and Gareth Barry, 35 next month, both excellent.
"Gareth Barry is one of those players that gets under-rated," said the Toffees boss.
"For me the big reason why we have so many effective young players is there are leaders in the mould of Gareth.
"I have never seen a player with such incredible professionalism
For me he is one of the best English players ever.
"He could end up with 600 Premier League appearances [by the end of] this season
You can build a team around him."
City boss Manuel Pellegrini has injury worries of his own after Eliaquim Mangala was substituted at half-time to join fellow centre-back Vincent Kompany on the sidelines.
"Yes of course it is a problem," he said.
"We have just two centre-halves, (Nicolas) Otamendi and (Martin) Demichelis, and we have to play six or seven games more in January
It is a lot of games."
Pellegrini was even less happy with the performance of referee Robert Madeley after he allowed Funes Mori's goal to stand despite Lukaku being in an offside position in front of goalkeeper Willy Caballero and then failed to award a penalty late on for a foul on Navas.
"The first goal is absolutely offside, Lukaku is one yard in front of Caballero and he makes the movement and then there is a clear penalty on Jesus Navas," he added.
"But the referee didn't whistle for both actions
We lost 2-1 but I think we are still able to play in the final of the Capital One Cup.
"Maybe everyone can have his opinion about every game, playing away, playing at home, it was not the score we wanted to have but it is the score that playing two legs, you can win."
Source : PA
Source: PA