Nishikori, the defending champion, had never faced the 165th-ranked Harrison before and was given something of a rude awakening as he lost the opening set 6-3.
Harrison claimed the lone break in the opener and did not have to save any break points, but he was under more pressure in the second set despite increasing his first serve percentage, with Nishikori breaking twice to take the second set 6-3.
The world number five struggled with his serve on the day, with first serve percentages of 48 percent in the first set and 44 in the second. However, he was able to up his game when it mattered, holding firm on his own serve after securing an early break in the decider.
Harrison refused to go quietly and at times threatened to break back, but he could not string enough points together to get back into the encounter, with Nishikori taking the match 3-6, 6-3, 6-4 in an hour and 57 minutes. Harrison will perhaps feel slightly unlikely, with the players ending the match having won the same amount of points.
Nishikori will face another American qualifier in the quarter-finals in the form of Austin Krajicek who accounted for number five seed Ivo Karlovic 7-6(4), 4-6, 6-4 earlier on Wednesday.
Sam Querrey also booked his spot in the last eight, defeating fellow American Jared Donaldson 6-4, 6-1.