By far the most experienced player remaining in the field after Harris's upset of Rafael Nadal on Friday (AEST), Nishikori prevailed 6-3 7-5 to avenge a loss earlier this year in their only prior meeting.
Nishikori had lost his past six ATP quarter-final matches dating to a trip to the semi-finals in Barcelona in April 2019.
The 31-year-old next faces Mackenzie McDonald, who downed countryman Denis Kudla 6-3 6-2 to reach his second career ATP semi-final. He has never played in a final.
In the other semi-final, No.5 seed Jannik Sinner will meet wild card Jenson Brooksby.
Sinner had little trouble with American veteran Steve Johnson in a 6-4 6-2 win as the Italian won 93 per cent of his first-serve points and saved all three break points he faced.
Brooksby maintained the strong return game that as carried him all week in a 6-1 6-2 upset of No.11 seed John Millman.
The Australian did not manage an ace against the 20-year-old American, who won 54 per cent of the points on Millman's serve and converted five of seven break points.
At No.130 in the world, Brooksby is the lowest-seeded Citi Open semi-finalist since John Isner reached the 2007 final when ranked No.416.