Ike Ugbo put the visitors ahead against the run of play on the stroke of half-time, only for City playmaker Phil Foden to level it up with a fine strike just after the hour-mark.
City bossed the opening exchanges but their highly rated keeper Aro Muric had to produce a fine save at full stretch to deny Callum Hudson-Odoi, who was lively all evening for the visitors, after 12 minutes.
The hosts had several chances to take the lead then on but Foden pulled a shot wide on 20 minutes, before Lukas Nmecha spurned two golden chances from tantalising Brahim Diaz through-balls.
Nmecha, who has scored 10 goals in the tournament so far, raced through onto the first pass but saw his shot graze the outside of the post when one-on-one with Jared Thompson in the Chelsea goal.
Three minutes later he was through again, but after turning his man on the edge of the box he fired wildly over the bar, provoking gesticulations from City boss Pep Guardiola, who was watching from the stands.
But just as City looked to be establishing a foothold on the match as half-time approached, Chelsea stepped up a gear.
Hudson-Odoi went close twice in two minutes, with his latter effort, from outside the area, hitting the outside of Muric's post.
But the Chelsea No.11 was in the thick of the action again shortly afterwards when he teed up Ugbo for the opening goal.
Hudson-Odoi's close range effort was diverted onto the post by Muric, but the winger collected the rebound, composed himself and played in Ugbo, who fired into the net.
Chelsea's Dujon Sterling blazed over from just inside the right side of the penalty box three minutes after the break as the Londoners went in search of a second, but City soon regained control of the tie.
Brahim took responsibility for City, dropping into midfield to collect the ball from his defenders and quickly turn defence into attack.
There were, however, few clear cut chances of note until Foden picked up the ball on the inside left, burst into the area and fired a clean strike into the far corner.
But with just under 30 minutes to grab a winner neither side were able to create the type of opportunities they managed to carve out towards the end of the first half.
The home side had the better of the match overall but Chelsea, who have won the competition three years on the bounce, were as dangerous a proposition as ever, meaning the final is in the balance ahead of the deciding leg at Stamford Bridge next Wednesday.