Cilic's meeting with Nishikori is a repeat of their 2014 US Open final which Croatia's Cilic won in New York.
Sixth seed Cilic is up to 12th in the race to reach the World Tour finals in London next month.
He needed only 74 minutes to overcome Johnson, and is chasing a place in the top eight that would see him qualify for the tour finals at the O2 on November 15-22 for the second straight year.
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Nick Kyrgios enjoyed a comfortable 6-4 6-2 win over Roberto Bautista Agut in just 57 minutes.
The Australian faces Benoit Paire, who completed a 6-3 2-6 7-5 win over Cypriot Marcos Baghdatis.
Qualifier Austin Krajicek was a 2-6 6-4 6-3 winner over Joao Sousa in reaching his second World Tour quarter-final where he will face a stern examination against French Open champion Stanislas Wawrinka.
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