Chelsea won 3-2 on aggregate after their 1-0 win at Stamford Bridge in the first leg.
In a pulsating match, Juve finished with 10 men following the second half dismissal of Giorgio Chiellini but goals from Vincenzo Iaquinta and evergreen Alessandro Del Piero had briefly given them hope.
Instead the first of three anglo-Italian ties in the second round went the way of the powerful Premier League.
Trailing 1-0 from the first leg and needing to score, Juve coach Claudio Ranieri picked an attacking line-up, with Del Piero playing behind forwards David Trezeguet and Iaquinta.
Even so, they did not create much until the 19th minute when the hosts took the lead out of nothing.
Iaquinta played a one-two with Trezeguet, whose return ball flicked over his head was perfectly weighted, allowing his strike partner to outpace John Terry and finish past Petr Cech with aplomb.
Juve suddenly had a spring in their step and Del Piero tried his luck from distance, forcing Cech to tip the ball over.
The hosts were looking comfortable and having the better of things without looking like adding to their lead.
But the game turned on its head in a crazy spell at the end of the first period.
On 45 minutes Drogba lined up to take a free-kick which he bent around the wall and just inside the post.
Gianluigi Buffon got across his line to clutch the ball at the post at the second attempt but television replays showed it had just sneaked over the line.
It wasn't given but Chelsea's frustration fired them up enough to equalise in first half stoppage time anyway.
Frank Lampard set his sights from distance and his shot took a deflection and looped up with Buffon arching back to tip it onto the bar.
It came down and may too have crossed the line but Essien charged in to bundle the ball home and leave no doubt this time that the Blues were on level terms.
It was his first goal in 11 months in his first start since September.
That changed the tone of the game and it took Juventus a full quarter of an hour of the second period to start looking dangerous.
When they did Del Piero was the architect of a move on 65 minutes that almost resulted in a goal as he crossed for Trezeguet to head goalwards, only for Cech to produce a flying save. Ranieri introduced young playmaker Sebastian Giovinco and he too almost created something but Del Piero couldn't quite get a flick on his team-mate's free-kick.
Any chance of a Juve revival seemingly died 20 minutes from the end when Chiellini picked up a second booking for clattering into Drogba.
But moments later Del Piero fired a free-kick into the Chelsea wall that struck Juliano Belletti's raised arms and the referee pointed to the spot, with Del Piero himself cooly slotting the ball home.
It was game on but seven minutes from time Chelsea sealed their passage into the last eight as substitute Juliano Belletti crossed for Drogba to poke home from close range for his fourth goal in five games.