The Blues made four changes from the 2-0 win in the first-leg, as Timo Werner, Romelu Lukaku, Andreas Christensen and Callum Hudson-Odoi were recalled while Spurs switched three places, with Giovani Lo Celso, Harry Winks and goalkeeper Pierluigi Gollini given a run.
Thomas Tuchel's charges were threatening in the early exchanges, with Lukaku denied by Gollini but the Italian shot-stopper made a blunder in the 18th minute after coming out and not collecting Mason Mount's cross from a corner and he was punished by Antonio Rudiger, who gave Chelsea the lead with a header and made it 3-0 on aggregate.
Spurs came close to finding the equaliser in the 32nd minute after Davison Sanchez's flick at the near post from a corner went through towards an open far post but Harry Kane could not adjust himself in time and missed the ball completely.
Antonio Conte's men had a penalty overturned by the Video Assistant Referee (VAR) just before the half-time break, as Rudiger's tackle on Pierre-Emile Hojbjerg was adjudged to be just outside the box.
The Lilywhites were threatening early in the second stanza and they had a penalty overturned again by the VAR just before the hour-mark following Kepa's challenge on Lucas Moura.
Spurs finally found the back of the net in the 63rd minute after Kane punished Kepa's misplaced pass but the goal was disallowed for offside on Moura.
The writing was on the wall in the closing stages for Conte's troops, with Chelsea's 3-0 aggregate lead proving a mountain to climb and they succumbed in the semi-finals, as the Blues marched on to the final to play the winner between Liverpool and Arsenal.