Having established a slender first-leg lead, Emerson Palmieri’s late strike sealed the win after Hakim Ziyech had earlier put the hosts firmly in control with a low effort after good work from Kai Havertz and Timo Werner.
Until then their dominance in possession had not translated into chances in front of goal, and in a nervy opening they also appeared fortunate to survive a penalty appeal after visiting winger Yannick Carrasco was pulled back by Blues captain Cesar Azpilicueta.
Italian official Daniele Orsato waved away the claim, and the incident was not examined by VAR.
Atletico knocked Liverpool out of the competition in dramatic fashion at the same stage last term, but the La Liga leaders rarely looked capable of recovering after Ziyech’s goal.
Instead Chelsea, who remain unbeaten in 13 games since Thomas Tuchel took charge, had opportunities to extend their lead before Emerson’s stoppage-time effort and deservedly progressed against an Atletico side that had Stefan Savic sent off late on for elbowing Antonio Rudiger.
The Blues join Premier League rivals Liverpool and Manchester City in the draw for the quarter and semi-finals on Friday at 11:00 GMT.
Summer signings set the tone
Efficient rather than entertaining has been the mantra since Tuchel took charge at Chelsea, with the club’s defensive solidity contributing to 11 clean sheets in their 13 matches in all competitions.
And while this performance can also be filed away under that description, it delivered a fine result against seasoned European campaigners.
Diego Simeone’s side may not be known for their flair or invention but they showed at Anfield just over a year ago how dangerous they can be.
However, Tuchel set his side up perfectly with N’Golo Kante and Mateo Kovacic stifling the space in midfield and using the ball intelligently when in possession.
Forwards Ziyech, Werner and Havertz were also integral in that regard, with one of the trio often triggering the Chelsea pressing game and setting the tone as they stifled their opponents.
Werner, who has endured a difficult time in front of goal since his switch to Chelsea, was particularly impressive.
Exhibiting pace and composure, the German forward accelerated onto a Havertz pass before superbly playing the ball into Ziyech’s path for the opening goal.
It proved a pivotal moment on the night and laid the platform for the assured way in which the Blues saw out the tie.
Disappointing Atletico
While Atletico can now turn their attention to holding off Barcelona and Real Madrid at the top of La Liga, this was another disappointing exit for a club that has reached the final twice in the past decade.
Simeone and his side have been known for revelling in these occasions, using their energy and application to often emerge as winners when tagged as the underdogs.
However, this performance exhibited few of those qualities and there was also a noticeable vulnerability in defence whenever Chelsea attacked with pace and purpose.
They were no better in attack. Luis Suarez, the man they had hoped could unlock Chelsea’s defence, was withdrawn before the hour mark after getting little change from Kurt Zouma, Rudiger or Azpilicueta and looking like a player very much in final stages of his career.
They were restricted to just a single chance of note in added time – when Joao Felix saw home goalkeeper Edouard Mendy save his fierce drive – underlining the gulf between the sides.
‘You need to feel it’ – what they said
Chelsea boss Thomas Tuchel: “The most important thing is that we feel we deserve this.
“It’s most important you feel it and that no one has to convince you – you need to feel it.
“They play with a special bond and performances and results like this give you a certain edge and glue to achieve special things. You can only achieve this through results and experiences.
“I’m pretty sure no one wants to play against us. It’s a super difficult challenge ahead because we are already in the last eight. It’s a big step, but no need to be afraid, we take what we get and prepare as best as possible.”
