Title holders Bayern Munich beat Lazio 2-1 and 6-2 on aggregate to reach the Champions League quarter-finals a record 19th time.
Robert Lewandowski converted a first-half penalty and substitute Eric Maxim Choupo-Moting got the second for Bayern who had effectively sealed the tie with a 4-1 win in Rome last month, DPA news agency reports.
Munich broke a tie with Barcelona as they reached the last eight a record 19th time since the elite event was rebranded Champions League in 1992-93.
Chelsea, meanwhile completed a 3-0 aggregate success over Atletico Madrid from a 2-0 victory courtesy of Hakim Ziyech in the first half and Emerson in stoppage time. The visitors had Stefan Savic sent off in the 81st.
Bayern and Chelsea completed the quarter-final field which also includes Liverpool, Manchester City, Borussia Dortmund, record winners Real Madrid, last year's finalists Paris Saint-Germain and Porto.
Semifinals on Friday
The draw for the quarter- and semi-finals is on Friday.
Alexander Nuebel got a rare start between the posts in snowy Munich to replace the ill Manuel Neuer, and Bayern with their three-goal cushion controlled the action as Leroy Sane curled just inches wide left in the 13th minute.
Sergej Milinkovic-Savic had a dangerous header for Lazio but Bayern were on top in the 33rd when Lewandowski converted into the bottom left corner from the spot after Leon Goretzka was pulled down by Vedad Muriqi.
Lewandowski hit the left post in the 66th, left the pitch five minutes later for Choupo-Moting who needed only two minutes to make it 2-0 by lobbing home off David Alaba's long ball.
Marco Parolo headed a late consolation goal for Lazio off a free-kick but Italy now has no team left in the competition as Juventus and Atalanta also went out in the last 16.
"It was important for us to win the game," Munich midfielder Joshua Kimmich told Sky TV. "You are aware of the first leg result but we were solid and in control. It wasn't a great match but we did a good job."
At Stamford Bridge, Atletico pleaded in vain for a penalty when Yannick Carrasco went down after being lightly pulled by Chelsea captain Cesar Azpilicueta.
The Spanish league leaders' misery grew when Chelsea opened the scoring in the 34th, with Timo Werner crossing low from the left on the counter for the Moroccan Ziyech to tap home between the legs of Jan Oblak.
Atletico now needed two goals but it was Chelsea who threatened and Oblak saved well from Werner's tight angle attempt right after the restart, and tipped Ziyech's curling effort over the bar in the 57th.
Joao Felix had a deflected shot go inches wide right at the other end before Savic got his marching orders for elbowing Antonio Ruediger.
Emerson then wrapped up matters into the far left corner in the stoppage time on his first touch after coming on late as Chelsea remained unbeaten in 13 games since Tuchel Tuchel became their manager in January.
"It was a bit like seeing how the game would go for 10 minutes and after that we had control. We did well. They didn't create a lot. We can be happy about the performance," Ziyech told BT Sport.
