Ernesto Valverde's charges came into the clash having secured a vital away goal in a 1-1 draw in the first leg at Stamford Bridge.
Barca got off to the perfect start when Lionel Messi combined with Luis Suarez before firing a shot under Thibaut Courtois from a tight angle with just over two minutes gone on the clock.
The Blues looked to hit back and went close through Willian, who forced Marc-Andre Ter Stegen into a fine save after 11 minutes.
Ousmane Dembele, who did not play in the first leg, doubled the home side's lead on 20 minutes with a powerful finish from inside the box after collecting a pass from Messi.
Antonio Conte's continued to push for a first goal and were almost reward before the break when Marcos Alonso rattled the upright with a free-kick from 20-yards out.
The Blues felt the should have been awarded a penalty four minutes into the second stanza after Gerard Piqué appeared to have pulled Alonso down in the box but the referee waved away the appeals.
Barça were struggling to get out of their own half towards as the visitors exerted a lot of pressure looking to get back into the match.
However, after working their way out, Messi got the ball on the edge of the box and skipped past two markers before slotting the ball through the legs of Courtois in the 64th minute to rack up his 100th goal in the Champions League.
Paulinho nearly made it 4-0 for Barça with a powerful header inside the box five minutes before time, but Courtois parried his effort over the crossbar.
Antonio Rüdiger’s header crashed against the underside of the crossbar in the closing stages as Barca managed to hold for the 3-0 win on the night and 4-1 win on aggregate.