Thiem, 24, won 6-4 6-2 6-1 against the German second seed.
The match started brightly, with the early signs living up to the thrilling contest that many were expecting, with Thiem securing the only break to go a set up. It's the best, a five-set match.
The Austrian blew the Monte Carlo finalist away within the first two units, misplaced the third, however got here by means of 6-2 6-Zero 5-7 6-Four to land in a 3rd consecutive Roland Garros quarterfinal.
Novak Djokovic equaled Roger Federer's mark of reaching nine consecutive quarterfinals, by beating No. 30 seed Fernando Verdasco 6-3, 6-4, 6-2. The Austrian began his tournament by defeating Ilya Ivashka of Belarus in straight sets 6-2 6-4 6-1.
If the match drags on and Thiem manages to take the lead, the mountain will probably be too high for Zverev to climb this time.
At world number 72, Cecchinato becomes the lowest-ranked man to reach the last eight in Paris since Latvian Ernests Gulbis (ranked 80) in 2008.
Djokovic, who missed the last half of 2017 with right elbow trouble and had surgery in February, is clearly not at the height of his power. "I knew I had to take risks", Cecchinato said. "It will be a pleasure to play against Novak".
For the former champion, though, it was not to be as he came up against the unseeded Marco Cecchinato in blistering form, and lost a gruelling and highly intense four-setter, 6-3, 7-6 (4), 1-6, 7-6 (11).
Goerges broke the 23-times Grand Slam champion in the fourth game of the second set to get back on level terms at 2-2 but her moment in the spotlight was fleeting as she dropped serve in the very next game and Williams roared on to an easy victory.
But he cut a forlorn figure as Thiem triumphed in one hour and 50 minutes.
If she wins that match, Keys could meet Stephens in an all-American semifinal.
"The first two sets were incredible but then he raised his level and it was 50-50", said Thiem of Nishikori.
The 12-time grand slam winner's subsequent challenger is not David Goffin however fairly Marco Cecchinato, who upset the ailing eighth-seed 7-5 4-6 6-Zero 6-Three after shedding to the Belgian final month. And the last 10 years you needed to beat at least two of them in a Grand Slam to win, and not many players did it.
"I think that's the matchup most of the fans in Germany and Austria were hoping for when they saw the draw", he said. It's something very special to serve for the French Open quarters.
Zverev's comebacks during this tournament have been marvellous to witness, but the real concern is whether he will have anything left in the tank to have a real shot at the title and whether he will be about to dig deep for a fourth time if he was to go down in the scoreboard to Thiem, who may not be as forgiving as his previous opponents this week.
"He deserves to be in the semi-finals".
On Court Suzanne Lenglen, Zverev's smash at the net gave him match point, which he took when Khachanov netted a forehand. He chatted with himself during changeovers - "I like to talk", he said later - and dropping down onto the red clay after one last backhand victor on match point. "This definitely paid off, the hours in the gym every day. So with this [aspect], I'm really happy".
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