Murray won 6-3 6-7 (5-7) 7-5 in two hours and 29 minutes in the French capital.
Jose Mourinho, Nick Kyrgios, Louis Smith and Sebastian Vettel tower over the governors of their sports.
The Wimbledon champion can become world number one with victory in the French capital.
Murray has an opportunity to beat Novak Djokovic to become the new world No 1.
Djokovic will face Muller in the 2016 Paris Masters on Wednesday.
Murray broke down following his heartbreaking loss to the Swiss star.
Djokovic has won just one title after his French Open success in June.
The Vienna Open champion could create history if he claims victory in the French capital.
Murray, 29, hopes to be the world number one by the end of 2016.
Kyrgios, 21, was recently banned and fined for tanking at the Shanghai Masters.
The result moves Murray one step closer to becoming the world number one.
Murray and Tsonga have faced each other 16 times so far, with the former winning on 13 occasions.
Rafael Nadal cut his season short after the Shanghai Masters earlier this month.
Murray won the match 6-1 6-3 in just 75 minutes.
Nick Kyrgios was banned for eight weeks for deliberately underperforming during a match.
Murray and Ferrer have won the Vienna Open in 2014 and 2015 respectively.
Jo-Wilfried Tsonga faces Ivo Karlovic in the Vienna Open semi-final clash on Saturday.
Murray has defeated Isner in their last six encounters.
The Briton came from a set behind to book his place in the quarter-finals.
Murray faces Simon in the second round of the Vienna Open. Find out where to watch live.
Roger Federer and Rafael Nadal will only be seen in action next year.
The 31-year-old Russian took a pair of scissors to her blonde locks.
WTA keeps her out as she has not competed in enough tournaments in 2016.
Roger Federer is currently recovering from surgery to his right knee.
Konta was poised to appear at the season-ending tournament in Singapore.
Federer has opted out of playing the rest of the season to work on his rehab from knee injury.
The Spaniard has endured a poor autumn and appears in pain when he plays.
Only Svetlana Kuznetsova can now stop the British No1 from sealing final qualification spot.
Kyrgios was suspended after tanking during the Shanghai Masters.
The 31-year-old is currently ranked 1,065 in men's singles ATP rankings.