Mourinho went all the way in this competition with Porto in 2004 and Inter in 2010 and is bidding to become the first manager to the lift the famous trophy with three different clubs.
After a 1-1 draw in Turkey in the first leg, first-half goals from Samuel Eto'o and Gary Cahill - on his 100th Chelsea appearance - sealed a comfortable 3-1 aggregate success for the Premier League leaders on Tuesday, with the long-awaited Stamford Bridge return of Didier Drogba proving an anti-climax.
Eto'o opened the scoring with the first attack of the game, controlling Oscar's pass before firing low into the corner and Chelsea made their dominance count shortly before the break when Cahill converted the rebound from a John Terry header.
Former Chelsea striker Drogba had very little impact on the game, his most notable contribution coming in the first half when he blasted a free-kick over the crossbar and into a banner bearing his own name.
Mourinho's spiky relationship with opposite number Roberto Mancini was well documented in the build-up, but it was the Portuguese who had the last laugh as Chelsea secured an untroubled passage into the quarter-finals.
Eto'o, back in the side in place of Fernando Torres from the first leg, had scored all of his previous nine Chelsea goals at home and that trend continued in the fourth minute.
Eden Hazard played a pivotal role, spinning away from Felipe Melo before feeding Oscar, who slipped the ball into the path of the striker, the Cameroonian taking a touch before firing low beyond Fernando Muslera.
Hazard and Oscar combined to great effect once again midway through the half to set up Frank Lampard, who stabbed his effort wide.
Chelsea went close again in the 33rd minute, Lampard whipping in a free-kick from the left that Terry volleyed narrowly over the crossbar from 10 yards.
The hosts continued to press with Hazard at the centre of everything, this time bursting down the left to allow Eto'o to set up Willian, but the Brazilian's tame effort was comfortable for Muslera.
All Chelsea's pressure paid off three minutes before the break, Cahill smashing home from close range after Muslera had parried Terry's powerful downward header from a Lampard corner.
Willian tested Muslera with a powerful drive five minutes after the interval, while the Uruguayan also denied Lampard and substitute Torres towards the end.
In stoppage time, Drogba fluffed a chance to trouble Petr Cech on the goalkeeper's 100th Champions League appearance as Chelsea reached the quarter-finals for the eighth time in the last 11 seasons.
