Germany and Qatar will meet on Wednesday night in what promises to be one of the tournament's best ties.
Germany, the 2007 world champions, had initially failed to qualify for this year's tournament but were reprieved after the Oceania region of the International Handball Federation failed to supply a team for the event.
And prior to Monday’s game they were one of just five unbeaten teams left in the competition, along with Spain, France, Croatia and Denmark.
Qatar have only lost once, and that narrowly, to current world champions Spain.
Germany quickly dominated the showdown with Egypt, taking control early on and leading 9-4 after just 19 minutes.
Germany went into the break leading 12-8, thanks largely to Patrick Groetzki's fine performance, scoring five goals from five shots.
Any hopes Egypt -- spurred on by a huge following at the stadium in Lusail -- had of reducing that deficit virtually disappeared within the opening 10 minutes of the second half when the Germans extended their lead to 18-10.
Still Egypt fought hard to reduce the gap but found Germany's defence, marshalled by Erik Schmidt, too hard to break down.
At the other end, Uwe Gensheimer ended up as top scorer with six goals.
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Schmidt said afterwards he expected the date with Qatar to be the "hardest game" the Germans have faced so far.
He said Qatar "have a good team, they have played a long time together, that will be hard to play against".
Germany's victory also stopped any chance of a politically sensitive quarter-final clash between Qatar and Egypt, who have endured fragile relations in the past year.
Qatar's Emir, Sheikh Tamim bin Hamad Al-Thani attended the match.
The team that knocked Germany out of the qualifying tournament to get to Qatar, Poland, also qualified for the last eight on Monday, scraping past Sweden.
They won 24-20 and their reward is a clash with Croatia on Wednesday.
There were no surprises in Monday night’s other ties.
Tournament favourites France eased through a potentially tricky-looking clash against Argentina, winning 33-20.
Meanwhile Denmark beat Nordic rivals Iceland 30-25.
Wednesday's quarter-final line-up is: Croatia v Poland; Qatar v Germany; Denmark v Spain and Slovenia v France.