Jesus Navas scored the potentially-critical away goal for City, with the second leg coming up on Jan. 27.
Sadly for Everton, fans may be just as distraught about Lukaku limping off the field after scoring as they are excited about being 90 minutes from the League Cup final.
[ LEAGUE CUP: Liverpool takes 1-0 away lead on Stoke in other semi ]
Funes Mori was in the right spot to tap Everton into a 1-0 lead just before halftime, as Ross Barkley‘s shot from outside the 18 was saved onto the doorstep by Wily Caballero.
Everton had a pair of first-half goals disallowed, but Funes Mori’s tap-in made sure the home side had a lead going into halftime.
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City came close to finding an equalizer midway through the second half, as Sergio Aguero took a touch but leaned back while blasting a 10-yard shot over the bar.
But a picture-perfect counter attack allowed Man City to capture a vital away goal. Fernandinho made a long, gorgeous pass that Sergio Aguero squared for Navas to work past Joel Robles. 1-1 in the 71st minute.
But Lukaku answered back moments later, heading a fantastic left-footed cross from Seamus Coleman past Caballero to make it 2-1.
Lukaku was injured on the play, and had to leave the game with a significant limp.