It is a repeat of last year's semi-final, which Murray won in four sets before going on to lose in the final.
Wawrinka, then the defending champion, was beaten 6-4 6-2 4-6 6-2 in 2016 before Murray lost to Novak Djokovic in the final - the Serbian completing a career grand slam in the process.
The Briton will now hope to replicate last year's win over Wawrinka at the same stage, one of his best performances on clay. "I'm happy to be into the semi-finals again, it's not always been easy for me, but the past few years have been great".
The 32-year-old Swiss took just 100 minutes to dispose of the 2014 US Open champion to reach the semi-final for a third time in a row.
These two have played 17 times, and Murray won 10 of those meetings.
Andy Murray is coming off a four set win over Kei Nishikori that took 35 games to decide. "We don't know what's going to happen on Friday, don't know how either of us are going to play, but with the right attitude, right game plan, right tactics, you can still win matches".
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A brilliant piece of trademark Murray scrambling helped secure the decisive break midway through the fourth set and Nishikori's challenge was as good as over.
He broke twice to win it 6-2 and then started off the second set promisingly.
Nadal criticised Ramos earlier in the tournament after also being penalised a first serve, saying he felt the umpire was looking for him to slip up, while the Portuguese official had a run-in with Djokovic as well.
"I have never had any issues with him before", Murray said.
"Obviously for a couple of points after that I was sacked up, because I was frustrated at that moment. It felt to me like it was a unusual decision", he said. "It was hard conditions but I got through it and finished strong". I have never seen that.
Murray said courtside: "I needed to put a little bit more pace on my shots".
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Murray will face 2015 champion Stan Wawrinka for a place in the final in Paris. Murray looks for his third grand slam final appearance since last season.
Andy Murray defeats Kei Nishikori to advance at Roland Garros.
Pliskova reached the U.S. Open final a year ago, but the Czech player had never been past the second round at Roland Garros in five previous appearances. The Romanian wasted four set points but evened the match on her next opportunity in the tiebreaker after saving a match point.
The third was a rather tight affair, with Murray breaking and serving for the set only for the 27-year-old to respond with a break back of his own.
The third seeds, who are unbeaten on clay this season, next face a tough test against top seeds Bethanie Mattek-Sands of the U.S. and Lucie Safarova of the Czech Republic, who ousted unseeded Francesca Schiavone of Italy and Kirsten Flipkens of Belgium 6-2, 6-4 in their quarter-final.
British Airways disruption continues for third day
At Heathrow, the airline restored long-haul services on Sunday but had to cancel some short-haul flights. All the airline's flights from Heathrow and Gatwick were grounded on Saturday, The Guardian reported.