Frenchman Simon was a physical wreck after Saturday's marathon third round victory over Gael Monfils and Murray barely had to move out of first gear to reach the quarter-finals on Hisense Arena.
Simon managed to force his spindly legs around the court to break the third seeded Briton twice.
The constant pressure on his own service gradually took its toll, however, and Murray swept into the last eight with his eighth break after a 95 minute encounter.
Murray, seeking his second Grand Slam title after winning last year's US Open, will next face unseeded Frenchman Jeremy Chardy as he bids to secure a fourth successive semi-final berth at Melbourne Park.
"It was kind of tough, a tough situation for both players - more obviously for him," Murray said.
"After the first few games, it didn't feel like that competitive. At this stage of a grand slam you're sort of geed up and prepared for a tough battle.
"That's why it becomes hard because the emotions aren't quite into it. You're not quite necessarily feeling pressure, but you're wanting to try to finish the match as quickly as possible."
Although he was not stretched by Simon, Murray was thankful that he was at least spared the sort of energy-sapping encounter that the world number one Novak Djokovic experienced in his five-hour match against Stan Wawrinka on Sunday.
"(Simon) got tested very hard in his last round and couldn't compete today (so) you can look at it both ways," Murray added.
"You just got to work hard on the days off, practice all the things that you need to do better, hope that when the time comes that when you're tested you play better.
"But I think this week, the first few matches... I think almost every single time when I've been broken, I've broken straight back, which is a good sign. Hope I can keep that up."
The curse of the difficult second album is a well known phenomenon in rock music, where bands invest sometimes years of effort into a successful first release and then struggle to produce enough quality material to back it up with their second.
Grand Slam titles have proved equally difficult to replicate for first-time winners and Murray is bidding to become the only player in the open era to immediately follow his maiden title with another at the next major.
To achieve the feat, he is likely to have to beat Roger Federer in the semi-finals and then overcome Djokovic in the final.
First, though, he must see off another French challenger in the unseeded Chardy, who won their meeting in Cincinnati last year for his first victory over the Briton.
Simon thought his compatriot might again prove a difficult obstacle for Murray to negotiate.
"Jeremy's very aggressive, he has a huge serve, huge forehand. He's able to hit winners at any moment," Simon said.
"It's gonna be interesting to see the beginning of the match, because if Jeremy manages to win maybe the first set, then I think anything can happen."
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