Morocco forward Ziyech grabbed his first goal since October to put the hosts ahead in the first half at Stamford Bridge.
Emerson came off the bench to score the late goal that sealed a comfortable 3-0 aggregate victory over the lacklustre La Liga leaders.
Adding to Atletico’s misery, Stefan Savic was sent off in the closing stages for elbowing Antonio Rudiger in the stomach.
While Chelsea were the superior side for long periods, Atletico could justifiably claim they should have had penalty for Cesar Azpilicueta’s challenge on Yannick Carrasco when the score was still 0-0.
That was the only major scare for Chelsea as they extended their unbeaten run to 13 matches since Thomas Tuchel replaced the sacked Frank Lampard in January.
Tuchel boasts the longest ever unbeaten start by a Chelsea boss after moving past Luiz Felipe Scolari.
Revitalised by Tuchel, Chelsea have conceded just two goals in his brief reign and are on a run of six consecutive clean-sheets in all competitions.
Leading Chelsea into the last eight for the first time in seven years is another feather in Tuchel’s cap as the German eyes a return to the Champions League final following his defeat with Paris Saint-Germain against Bayern Munich last season.
Chelsea, Champions League winners for the only time in 2012, had been eliminated in the first knockout stage in their last four appearances.
But they never looked in danger of losing the 1-0 lead given to them by Olivier Giroud’s overhead kick in the first leg in Bucharest.
– Azpilicueta escape –
Crucially, Azpilicueta escaped without punishment when the defender’s under-hit back-pass allowed Carrasco to nip ahead of him in the penalty area.
Azpilicueta responded with a panicked tug that sent Carrasco tumbling but Atletico’s penalty appeal was controversially rejected by referee Daniele Orsato, with VAR bizarrely opting not to intervene.
Atletico boss Diego Simeone was furious and his anger only increased as Chelsea made the most of their good fortune to take the lead in the 34th minute.
Timo Werner, signed from Bayer Leverkusen to much fanfare in the close-season, now has just two goals in last 27 appearances for Chelsea.
But Tuchel backed Werner to come good this week and the Germany forward repaid his manager’s faith with a strong performance capped by the key contribution to Ziyech’s opener.
Breaking at pace after Werner blocked Kieran Trippier’s cross, Kai Havertz fed his team-mate on the left flank.
Werner accelerated away from the out of position Atletico defence before clipping a perfectly-weighted pass into Ziyech’s path.
Unmarked 10 yards from goal, Ziyech finished Chelsea’s rapier thrust with a clinical strike.
After struggling for much of their first season with the Blues, Havertz, Werner and Ziyech had finally combined to show why Chelsea spent over £150 million ($179 million) on them last year.
Joao Felix tried to drag Atletico back into the tie, but Edouard Mendy was equal to his deflected shot.
Werner’s pace was causing Atletico problems and he scampered clear for a low drive that Jan Oblak saved at his near post.
Oblak made an even better stop when he stretched to tip over Ziyech’s dipping effort from the edge of the area.
When Mendy denied Felix, Chelsea could see the finish line and Savic’s frustration boiled over in the 81st minute as he was dismissed for a needless elbow that drew a theatrical fall from Rudiger.
With Chelsea’s injured defender Thiago Silva roaring on Emerson from the stands, the left-back blasted home from Christian Pulisic’s pass in stoppage-time, sparking a wild celebration that encapsulated the feelgood factor fuelling the Blues at present.