Goals from Nathan Baker, Alex Kiwomya and Islam Feruz see the impressive Blues weather a second-half fightback to book their place in the last four of the competition
First-half goals from captain Lewis Baker and Alex Kiwomya put the Blues firmly in control and Islam Feruz and Baker made the game safe late on after Daniele Rugani's header had given the Italians hope.
The result keeps alive the possibility of two all-English semi-finals, with Arsenal, Tottenham and Aston Villa still to play their quarter-finals against continental opposition.
In a bright opening for both sides, it was Juventus who fired the first shot in anger, with Eric Lanini unleashing a curling effort from outside the box which narrowly missed the top corner.
But Chelsea were dominating possession and, on 10 minutes, Baker capped a flowing move with a fierce, dipping drive which found the top corner.
The Blues had struggled to create chances against the disciplined Italians early on but, only three minutes later, they doubled their lead with a lightning counterattack.
Winning the ball just outside his own penalty area, Andreas Christensen played the ball up to Feruz who, after waiting for support, fed Kiwomya to calmly dink the ball over Constantin Branescu.
Chelsea were well on top now and, on 17 minutes, Ruben Loftus-Cheek smartly picked out Adam Nditi on the edge of the area, but the winger shot just wide.
On 23 minutes Loftus-Cheek went close himself, winning possession in the Juventus half before advancing and unleashing a venomous effort from 30 yards which flew narrowly over.
Feruz then twice warmed the palms of Branescu before Nathan Ake almost deflected Elvis Kabashi's shot into his own net but Jamal Blackman made a fine reflex save and the Blues led at the break.
Juventus began the second half with intent, pressing much higher up the pitch, but a disciplined Blues defence marshalled by the impressive Ake prevented them from creating many real chances.
Stefano Beltrame did manage to test Blackman on 56 minutes, however, escaping the attentions of Ake and unleashing a low effort which the Chelsea goalkeeper blocked with an outstretched leg.
But the visitors kept pushing and, on 71 minutes, they found a way back into the game, as Rugani met Beltrame's inviting free kick with a glancing header which left Blackman helpless.
Chelsea briefly looked rattled but, as the Italians pushed forward in search of an equaliser, Kiwomya raced down the right before squaring for Feruz to seal the win.
And, with the home crowd already celebrating, substitute Charlie Colkett chipped the ball into the path of Baker, who grabbed his second to add another layer of gloss to an impressive victory.