The No. 3-seeded Wawrinka edged French favorite and No. 15 seed Gael Monfils 7-5, 7-6 (7), 6-2, while Cilic benefited when opponent Kevin Anderson of South Africa retired trailing 3-6, 0-3.
But things are more even in Grand Slams with both players having won one match.
Murray's reward is a reprise of last year's US Open quarter-final against Kei Nishikori - a dramatic match in which a random belch of noise from the PA system on Arthur Ashe Stadium triggered a switch in momentum, and an exhausting five-set win for Nishikori.
The World No.1, runner-up to Novak Djokovic in 2016, brushed aside Karen Khachanov of Russian Federation 6-3, 6-4, 6-4.
Nishikori has had a more gruelling passage to the last eight: he has twice lost a set 6-0, appears hindered by back trouble and will need to play as he did in NY to topple the rapidly improving world number one. And while that may be ludicrous to say of a three-time Grand Slam victor and world No. 1, he was written off by plenty before a ball was struck at this French Open.
"We have played so many times".
"I think today was probably the best I have played overall".
"It's never fun to lose a match, but I took a great experience from this match to play on the center court", he said. I don't know how I got the second and third sets.
Andy Murray racked up his 650th career win to reach the French Open quarterfinals Monday before paying an unscripted, emotional tribute to the victims of the London and Manchester terror attacks. Paris has also had some problems in the last (few) years.
"Certainly, I feel fresher than a year ago", Murray said.
There's a lot more experience and hardware among the remaining men.
"Actually I'm very bad with the memories", Nishikori said.
No 2 seed Djokovic will play Dominic Thiem of Austria in the first match on Suzanne-Lenglen, while Nadal, the nine-time champion, meets compatriot Pablo Carreno on Philippe-Chatrier.
He said: "It was a really close two sets".
Halep set up a quarter-final clash with Elina Svitolina, who clawed her way back from 5-2 30-0 down in the third set to defeat Croatian qualifier Petra Martic 4-6 6-3 7-5.
It's gala time at the French Open with the world champions' dinner taking place in Paris later Tuesday.
Nishikori, a beaten quarterfinalist here in 2015, has now made the last eight of a Slam for a seventh time, a record for a Japanese man. She fought off break point to hold at the start of the second set and then immediately broke. In another quarterfinal, Pliskova meets No. 28 Caroline Garcia, a 6-2, 6-4 victor against Alize Cornet in a match between two Frenchwomen. "Over the best of five sets Andy is going to be very hard to beat here".