The fourth seed looked rampant from the start and broke the Frenchman in the second game thanks to some clinical ground strokes which outfoxed his injury-ravaged opponent.
Murray wrapped up the first set in 23 minutes and the match continued in much the same vein in the second.
An early break of serve allowed the Scot to seize theÃ‚Â initiativeÃ‚Â once more and a first serve percentage of 65% was enough to prevent Simon from mounting a challenge as the Brit took the second 6-4.
Simon, previously ranked sixth in the world last year before suffering a knee injury, mounted a comeback of sorts in the final set, but the Frenchman became infuriated as his best efforts failed to trouble the enigmatic Scot.
With darkness filling the court and the threat of a 30-minute break needed for the potential deployment of the roof, the British number one seized upon a break point in the eighth game.
Murray successfully served out the match to set up a fourth-round encounter with QueenÃ¢â‚¬â„¢s Club champion Sam Querry, who had beaten BelgiumÃ¢â‚¬â„¢s Xavier Malisse earlier in the day.
“Tonight was tough because it was getting pretty dark towards the end and if I hadn’t closed it out in the third set I would have had to go off and wait for the roof to close, so I got a little bit tentative around 3-3,” Murray said afterwards.
And the fourth seed was delighted by his supreme form in the first week at SW19.
“It was really good,” he continued. “I didn’t lose a set and didn’t lose my serve since my second service game of the first match.
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BIOGRAPHY: Ethan Hazard
BIOGRAPHY: Daniel Sturridge