Dimitrov had won their only meeting this year in Miami and came into the match talking of a return to form, but he troubled Murray for barely a handful of points.
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The 21-year-old would have cause to feel very hard done by were he to miss out in Glasgow having reached the fourth round of the US Open but Evans has also staked a strong claim.
The world No. 2 was a set and a break up before the roof was closed on Arthur Ashe Stadium due to rain.
As Williams, never seriously challenged in a 6-2, 6-3 victory over 52nd-ranked Yaroslava Shvedova, sailed on, one of the two players with a chance to topple her from the world No 1 spot in this tournament bowed out as fourth-seeded Agnieszka Radwanska was shocked 6-4, 6-4 by 18-year-old Croatian Ana Konjuh.
Since the professional era started in 1968, only Djokovic (2015), Roger Federer (2004, 2006 and 2007) and Rod Laver (1969, when he completed a calendar-year Grand Slam) have been to a season’s four major title matches.
Murray now faces Nishikori, who was impressive against Karlovic in their fourth-round bout, coming out on top 6-3 6-4 7-6 (7-4). “I’m very proud of how I have done”.
Murray eased through to the US Open quarter-finals on Monday night with a thumping win over Grigor Dimitrov while Jamie Murray is through to the last eight of the doubles.
The British tennis superstar has won seven out of eight games against Japanese wonder Nishikori.
“Today I ran out of fuel, I think, physically and mentally”, said the Bulgarian. When you don’t play your best and win, it’s a really positive thing.
“They stopped the point and I was just curious why that was and that was it”, Murray said.
Speaking after his win, Murray said: “I played extremely well, tactically it was a good match”.
Del Potro is also into the quarter-finals in NY and their participation in Scotland could depend on their progress at Flushing Meadows.
Serving for the match, this time Nishikori did not waver as a Murray backhand dropped into the net and confirmed defeat after three hours and 58 minutes.
“His belief is higher than it’s ever been”, seven-time grand slam champion John McEnroe said on ESPN.
“It happens sometimes. I have won a lot over the last few months, but couldn’t quite get it going my way today”.
“He’s obviously, I think, playing pretty well this summer”. “I tried to stay positive and I knew that if I did, I could just stay in the match”. I’m aware I’ll need to do that again in a couple days if I want to beat him, because he’s one of the best players in the world. “I served very well when I was behind in the game”.
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The first two quarter-finals take place on Tuesday when reigning champion Novak Djokovic faces France’s Jo-Wilfried Tsonga and Lucas Pouille, the conqueror of Rafael Nadal, tackles French compatriot Gael Monfils.
