The unseeded pair played out a tight, two-set match in the first quarter-finals of the day. Dimitrov needed three sets to get past youngster Daniil Medvedev, while Lopez saved a match point to overcome Berdych in a tussle dominated by serve.
Cilic, the highest seed remaining in a decimated field, ran down American teenager Stefan Kozlov 6-0, 6-4, with the Croatian titleholder from 2012 striking in excess of 25 winners and never facing a break point.
Later, Sam Querrey, champion in 2010, plays Murray's conqueror Jordan Thompson while Feliciano Lopez takes on Jeremy Chardy.
With no break points created by either player in the first set, the second settled into a similar pattern as thunderous serves continued and another tiebreak followed.
Cilic, who also finished as Queen's runner-up in 2013, was pushed hard by Young, but the former US Open champion fired 11 aces to see off the American world number 55 in one hour and 26 minutes.
The 34-year-old Muller hopes to reach his fourth final this campaign after clinching Sydney and Den Bosch last week.
"I'm going to play semi-finals here for the first time tomorrow".
"Those are things you dream of as a kid, so when it happens it feels good".
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Lopez, who lost the 2014 final to Dimitrov, took nearly two and a half hours to progress with a 7-6 (7-5) 6-7 (1-7) 7-5 victory that lasted deep into the evening in London.
With Medvedev suffering a shoulder injury during the pre-match warm-up and needing lengthy treatment before he could start playing, it was no surprise Dimitrov won the first set after sprinting into a 5-0 lead.
Kokkinakis eliminated Milos Raonic in round one but Medvedev proved too strong as he set up a meeting with sixth seed Grigor Dimitrov.
Dimitrov, the 2014 Queen's champion, will be looking to reach his third ATP Tour final in 2017.
"It was tough out there, it was windy", the American said.
"I was prepared fully, I approached it in the best possible way for me".
"I'm really happy I was able to go one step further". "I'm not necessarily feeling great (on court) yet".
Being big was the theme today at Queen's with three players 6-foot-6 all advancing to the quarterfinal round.
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