Simon was taken to five gruelling sets by compatriot Gael Monfils in the previous round in a match which drifted into the early hours of Sunday morning and, having battled gamely, tired as the contest went on.
Murray still had to put him away but managed with ease to advance 6-3 6-1 6-3 in one hour and 35 minutes and improve his head-to-head record with the 28-year-old to 10 wins from 11 meetings.
"No one knew what to expect (from Simon) but I just had to focus on my side of the court," said Murray, who will meet another Frenchman, Jeremy Chardy, in the last eight.
"He's one of the best movers on the tour but he was struggling today.
"That's what grand slam tennis is all about, it's tough."
It was hard to gauge the performance given his opponent's limitations but Murray will be pleased to have made it this far without overly exerting himself.
Murray was having few troubles on serve, though, and held with ease to make Simon serve to stay in the first set at 3-5.
And he was unable to do it as Murray broke for a third time to move ahead.
Simon's weakened serve was not giving him any freebies with Murray able to work his way into every point.
And from there the Scot was happy to rally, moving his opponent round the court, knowing his energy reserves were low.