Murray won the game in just over two-hours, after defeating the Bulgarian 6-1, 6-2, 6-2 at the Arthur Ashe Stadium.
Murray is wary that Nishikori will back himself at Flushing Meadows, where the Japanese has reached his only Grand Slam final, but Murray believes he has recaptured his own best tennis ahead of the quarter-finals on Wednesday.
He played well in various areas, certainly, but also faced little resistance from No. 22 Dimitrov, who had accumulated 23 unforced errors and only two winners by the time he trailed 3-0 in the second set.
Murray is in the midst of his own golden patch with Ivan Lendl, under whom he has still only lost one match, but even in his runs to winning Wimbledon and the Olympics, it is hard to recall a more convincing performance.
The 2009 US Open champion, given a wild card in this US Open and ranked only 142 at the moment owing to persistent wrist injuries, entered the quarterfinals after Dominic Thiem retired due to a knee problem.
According to Matt Wilansky of ESPN.com, this is the sixth time Murray has won a Grand Slam match while losing five or fewer games. "He had a couple of breakpoints in the first game but once I got up in the score, wasn't giving him any free points, I could sense it was getting tough for him".
The Swiss needed a tiebreak fourth set to advance.
Dimitrov broke only once in the match in the fourth game of the second set but it was a brief respite as Murray quickly reclaimed it before taking 10 of the next 12 games to seal the rout.
Del Potro will face fellow Grand Slam title victor Stan Wawrinka for a semi-final spot.
"We'll wait for the players to arrive in Glasgow and see what state they're in", British captain Smith said.
The third seed looked to be in cruise control when he opened up a two-set lead for the loss of only five games, but he was sloppy in the third before regaining his rhythm to progress 6-4 6-1 6-7 6-3.
Of today's fastest serve, Murray said: "I think that was lucky". At 5-all, 30-all, Murray double-faulted to set up break point, and Nishikori converted by reaching for a stretch volley victor.
It's del Potro's first Grand Slam quarterfinal since 2013 Wimbledon semifinal run. Wawrinka overcame a third set dip to beat Illya Marchenko 6-4, 6-1, 6-7 (5-7), 6-3.