Thiem, who reached the semi-finals a year ago when he lost to Djokovic, will face nine-times champion Rafa Nadal next.
8 Kei Nishikori 2-6, 6-1, 7-6 (0), 6-1 on Wednesday, while No. 3 Wawrinka won 6-3, 6-3, 6-1 against No. 7 Marin Cilic. Murray leads their head-to-head series 10-7, including a four-set victory in last year's French Open semifinals.
Second-seeded Karolina Pliskova advanced to the semifinals of the French Open by beating No. 28 Caroline Garcia of France 7-6 (3), 6-4.
Murray, who arrived in Paris on the back of a woeful claycourt season, said he could take a lot of positives from his run to the semis.
Thiem had beaten Djokovic so fantastically in the quarter-finals, but was bagelled in the final set - as he had done to the Serb - and was simply second best throughout.
Defeat also meant that just 12 months after holding all four Grand Slam titles, the 30-year-old was left fighting to prove he is still a relevant force in the sport.More news: UFC Champ Max Holloway Says Conor McGregor 'Can Beg To Fight Me'
Nadal is yet to drop a set and has lost just 29 games in six matches - his lowest tally ever and the least since Bjorn Borg in 1978.
His Masters clay court swing saw him exit in the third round in Monte Carlo and Madrid and lose his opener in Rome.
Now only Stan Wawrinka remains between the 31-year-old and another record as the first man to reach double digits at a single slam.
Nadal, meanwhile, is the hot favourite to collect an unprecedented 10th French Open and 15th career major.
He trails Murray in head-to-head meetings 10-7 and lost to the Briton in four sets in the semi-finals a year ago. "He's had two tough weeks but he hasn't overplayed, so I don't see any negatives - I see positives".
"Maybe the lack of matches hurt me a little bit in the end today", Murray said.
With Nadal locked in, the Spaniard calmly converted the first of three set points with a confident volley to leave Thiem staring into the abyss. The Austrian was untroubled after he won the first-set tiebreaker enroute to his 7-6 (5), 6-3, 6-0 win over the defending champion.
Thiem must try to prosper where so many have tried and failed as he bids to conquer the Nadal forehand at Roland Garros. The world number one is two matches from his first win at Roland Garros and faces Stanislas Wawrinka for a place in his second straight final on Friday (9 June).