Both Sebastian Korda and Carlos Alcaraz won all three of their matches in the round-robin group stage.
Djokovic famously came back from two sets to love down to beat Greece's Tsitsipas at the French Open final to win his second Roland Garros.
Paul, ranked 52, beat three-time major winner Murray 6-2, 3-6, 6-3 and will take on compatriot Frances Tiafoe for a place in the final.
Murray, now ranked a lowly 143 in the world, will face Tommy Paul of the United States for a place in the last-four.
The injury-hit 34-year-old, still bidding to climb from his current lowly ranking of 143, will face Italian top seed Jannik Sinner in the last-16.
Paris Masters: Novak Djokovic survives Marton Fucsovics scare on tour return, Auger-Aliassime beats Mager
Djokovic endured a tough return to the ATP singles circuit but battled through to beat Marton Fucsovics of Hungary 6-2, 4-6, 6-3 in the second round
Murray, ranked 144, had been given a wild card but while the 34-year-old lacked killer instinct, he did show steely determination to battle back from a set and a break down to take the match to a third set before Koepfer won 6-4, 5-7, 7-6 (11/9).
There have been mixed messages over who will be allowed to play in the first Grand Slam of next year which runs from 17-30 January in Melbourne.
The 34-year-old Scot Andy Murray has tumbled down the world rankings after a series of career-threatening hip injuries.
Tiafoe, the world number 49, clinched a hard-fought 3-6, 7-5, 6-2 win to reach his first final of the season where he will face German second seed Alexander Zverev who downed Spanish teenager Carlos Alcaraz 6-3, 6-3.
The 18-year-old Alcaraz easily took the first set, lost the second on a tie-break before sealing victory over the Wimbledon finalist Matteo Berrettini on his third match point in the third-set tie-break.
Kooyong president Adam Cossar said he was disappointed the event could not take place in January 2022 but hopes it will return in 2023.
The three-time Grand Slam champion, whose ranking has tumbled to 156 after a series of injuries, will meet teenage Spanish star Carlos Alcaraz in the second round
Sinner entered the tournament ranked 13th in the world ad 11th in the race to the year-end Masters, an eight-player event which in Turin on 14-21 November.
Brooksby, a 20-year-old from California currently ranked a career-best 70th, reached the final four at an ATP tournament for the third time this season.
At 3hr 45min it was the longest best-of-three match this year, the ATP said, eclipsing the 3hr 38min played by Rafael Nadal and Stefanos Tsitsipas in the Barcelona final in April.
Last October, Sharypova accused the German tennis star of physical and emotional abuse, claims he has repeatedly denied.
Ruud, who had won only one ATP title before this year, became the first player to win five titles this season.
Andrey Rublev set up a showdown against Cameron Norrie of Britain, who scored his second straight upset win over a seeded player this week, defeating No 4 Denis Shapovalov