The Briton won 6-3, 6-4 in a match where both men played some superb tennis but Murray was far more consistent and had more winning shots to call upon.
Victory set up a meeting with Janko Tipsarevic, the ninth seed, in the last eight later today.
However, such a straightforward victory did not seem likely in the first game.
The third point of the match was a 40-shot rally, won by Simon, in what was a closely-fought game, the Frenchman pressurising Murray from the outset on his serve.
Simon brought up his first break point with a backhand down the line which was centimetres in but he could not take advantage.
Eventually the Scot went 1-0 up when he forced Simon out wide after a game lasting more than 17 minutes.
"I felt fine from the start of the match," the British No 1 said. "Probably the first game probably helped with that as well because I saved a couple of break points, there was a lot of long rallies, a lot of moving.
"After that, I kind of loosened up a little bit; felt much better.
"So that first game, even though it was like 17, 18 minutes, was probably a good thing after not playing for a few days."
Simon held his first service game to love, but, after holding, Murray then broke to love for 3-1 before dominating similarly to move further ahead.
Simon was not playing at all badly but rather everything Murray was trying was, for the most part, coming off.
The Frenchman played a bold game when he was 0-30 and 1-4 down to reduce the deficit but Murray was in control and moved on to 5-2.
Simon held to stay in the set, but a volley at the net gave Murray three set points which he took at the first time of asking with an ace.
The match went with serve at the start of the second before in the fifth game Murray brought up triple break point with a superb cross-court drive, but the Frenchman managed to dig himself out of the hole to hold.
Murray again moved to triple break point in Simon's next service game and this time converted for what proved to be the decisive blow, ultimately clinching the match with an ace.