Murray, the top seed and world number two, won 4-6 6-2 6-2 and will face American John Isner in the last eight.
The Scot, 29, could be within sight of the world number one ranking if he wins the title in Austria on Sunday.
Another victory at next week's Paris Masters would mean Novak Djokovic must have made the semis to retain top spot.
Murray has now won his last 12 matches, taking in titles in Beijing and Shanghai as he tries to capitalise on a chance to finally top the rankings.
That winning run looked to be coming to an end when Simon took the first set, after Murray managed just five winners to 24 errors, and then broke early in the second.
Murray looked weary on the slow Vienna surface but dug deep, saving six break points in a 14-minute game on his way to clinching the second set.
Simon then required heavy taping over a large blister on his foot and Murray took the third to win in two hours and 41 minutes.
That winning run looked to be coming to an end when Simon took the first set, after Murray managed just five winners to 24 errors, and then broke early in the second.
Murray looked weary on the slow Vienna surface but dug deep, saving six break points in a 14-minute game on his way to clinching the second set.
Simon then required heavy taping over a large blister on his foot and Murray took the third to win in two hours and 41 minutes.
