In baking conditions, the world No 4 rarely extended his record to 7-1 against Simon, but struggled with his serve and his ground strokes at times before finding some consistency in the second set.
Murray had to encounter a handful of shaky moments in a match that was played at a slow, often mundane pace, but a gradual improvement in his first-serve percentages – he won 78 per cent of the points on it – saw him home in an hour and 35 minutes. He will meet either Rafael Nadal or Mardy Fish in today’s semi-final.
After a delayed start because of a fire alarm, Murray appeared to have laid down an early marker when he broke serve in the opening game, eventually taking a fourth break point, only for Simon to instantly break back, showing his mettle to take a 37-shot rally.
Murray broke again in the fifth and after earning himself three set points on Simon’s serve, took the first set 6-3.
Murray’s serve came under threat in the third game but he quickly got a grip of things and then broke Simon to go 3-1 up.
A routine service game took him to within two games of the last four, and, after a hold apiece, he duly booked his place with well-timed drop shot.
Murray said that he had shown some early caution in order to get a foothold in the game.
“I have to play my game against him and it works very well,” he said. “I`ve seen many players try to blast him off. You have to wait for the right moments.”