The Austrian seventh seed, the last man to beat claycourt machine Rafa Nadal on his favourite surface, displayed an impressive arsenal of weapons in the first two sets before regaining his composure after the loss of the third.
Japanese 19th seed Nishikori, on the comeback trail after he ended his 2017 season in mid-year because of injury, seemed to lose interest in the match in the second set but eventually managed to put up a decent fight.
"The first two sets were amazing but then he raised his level and it was 50-50. In the end it was very close and I was a bit nervous in the end as it is always hard to serve to reach the quarter-finals of the French Open," said Thiem, a semi-finalist here in 2016 and 2017.
"I love these conditions; it was the first time for me on Court Philippe Chatrier not playing against Rafa so I could enjoy the court", he joked.
Thiem had too much power and speed for Nishikori, who was overwhelmed in the opening set, which the Austrian bagged with an ace in under half an hour.
It got even worse for Nishikori in the second set as Thiem toyed with him, notably with a stunning drop-shot service return, and the Japanese could manage only nine points in the set.
In the first two sets, the Austrian won 25 of 25 points on his first serve.
In the third set, however, Nishikori stayed in touch as he served better and finished off points at the net, which unsettled Thiem who grew frustrated.
Nishikori seized his first break opportunity at 6-5 to take the set when Thiem's forehand flew long.
The Austrian, who ended 10-times French Open champion Nadal's streak of 50 consecutive sets won on clay in Madrid, broke decisively for 4-3 in the fourth set with a trademark forehand winner.
He then held serve throughout to wrap it up on his second match point when Nishikori sent a forehand long under the eyes of Nadal.
German Zverev is expected to provide a much tougher challenge in the last eight, however.
"I think that's the matchup most of the fans in Germany and Austria were hoping for when they saw the draw," said Thiem.
"So it's going to be a very nice match again. Of course, for both of us I think we would have been very happy if we both went through this stage where we are now.
"And it's going to be great. We just played in Madrid. He's an amazing player. I mean, probably now the third best after Rafa and Roger (Federer). So it's going to be an amazing challenge for me."
(Editing by Clare Fallon)
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