The Japanese number one came out the blocks firing in the opening tussle of the afternoon on Court 2 and dominated the big-serving lefty from start to finish.
He quickly asserted his superiority in the opening set, breaking twice in quick succession to claim the first set in a tick over half an hour and, thereafter, the contest was only heading in one direction.
The world number 28 briefly regained his composure in set two but could not withstand the wave of Nishikori groundstrokes.
The American Donald Young awaits in the last 16.
Quick out the traps
Nishikori holds a positive 3-0 head-to-head record against the 33-year-old but was given a scare in their previous meeting on the indoor hard courts of Basel in the fall of 2016.
Muller took the opening set that afternoon and has been a steady presence in the top 30 since he claimed his maiden ATP title in Sydney earlier this year.
Indeed, he staved off the threat of the Czech Jiri Vesely in the second round on Sunday and the oven-like conditions in the Californian desert would ensure Muller’s serve contained an extra zip.
He began the contest strongly, holding to love in his opening service game and rallying well from the baseline as the Japanese leveled the score count.
But that would be his high-point for the afternoon, gifting Nishikori the all-important break with an errant forehand.
The world number four had produced a sumptuous backhand pass in that service game and his showman-like side was on full display when he held for 3-1 with a pair of supreme forehand winners.
A double break quickly followed, with the Japanese stretching his opponent from pillar to post before controlling a tricky overhead that had the admittedly sparse crowd on their feet.
He forced Muller to serve to stay in the set with a service hold that barely spanned a minute and, despite the Luxembourg restoring a modicum of pride, Nishikori claimed the set in commanding fashion.
More of the same
Muller’s box looked on in puzzlement and their anguish was set to exacerbate when Nishikori, his level refusing to dip, broke the 33-year-old to open set two.
The double-faults were beginning to creep into Muller’s performance but he steadied the ship to hold for 1-2 despite the narrative of the opening set.
The Japanese was toying with his opposite number, displaying excellent feel at the net and producing successive lobs that drew a gasp from those in attendance.
Muller offered brief resistance, fashioning a break point of his own in the sixth game but sending a backhand down the line just narrowly wide.
Nishikori held for 4-2 and, sensing an opportunity, manufactured three break points on the veteran’s serve.
Consecutive double-faults later, the Japanese was heading to the changeover with a 5-2 buffer and a chance to serve for a last 16 berth.
Behind his own serve, as he did all afternoon, he did not disappoint.