The French Open champion Wawrinka had lost to the Japanese player a year ago at the same time.
"It was a tough match and after losing to him last year, I am happy to have gotten through," said Wawrinka.
"I tried to mix up my play in the third set to move him around more. I have one day off now and will train to be ready for my next match."
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The Swiss player will face Joao Sousa or qualifier Austin Krajicek in Friday's quarter-finals.
Sousa overcame seventh seed Feliciano Lopez 6-4 4-6 6-1.
Third seed Gilles Simon was a 6-4 6-2 winner over Jiri Vesely in 76 minutes. He will face Gilles Muller who enjoyed a 7-6 (7-3) 7-6 (7-5) win over Jeremy Chardy.
Kei Nishikori boosted his prospects of qualifying for the World Tour finals at the O2 next month with a 7-6 (7-3) 6-3 win over Sam Querrey in 74 minutes.
He faces former US Open champion Marin Cilic on Thursday after the sixth seed completed 7-5 5-7 6-4 win over Donald Young in two hours and 39 minutes.
"He was playing really well," said Cilic. "It was windy and I struggled with my serve in the third set."
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