Zverev topples Tsitsipas at Paris Masters as Rune stays in hunt for ATP Finals
Zverev's 7-5, 6-4 win over Tsitsipas kept him in the running to claim his first title in Paris after losing to Daniil Medvedev in the 2020 championship match.
World number three Zverev - the highest-ranked player left in the draw - will face 2022 champion Rune in Saturday's semi-final after the Dane overcame De Minaur 6-4, 4-6, 7-5.
The 16th meeting between the German and Greek was evenly matched during a hard-fought first set.
"At the beginning, he was outplaying me but then I found my rhythm from the baseline," said Zverev on court.
"And when I had my chance I used it in the first set."
Indeed once Zverev broke late in the opener and early in the second, it became a comfortable ride to just his sixth win against his long-time Greek rival.
The loss ends the chances of the world number 11 Tsitsipas of reaching the end-of-year ATP Finals - having won the showpiece event in 2019.
Tsitsipas and Zverev started cautiously with both offering up opportunities for early breaks in their first service games.
But they soon found their range as the first set looked destined to require a tie-break to separate the pair on the quick surface at Paris' Bercy Arena.
However, the first break points of the match eventually came with Tsitsipas serving at 5-5, the German claiming the second on a double fault.
The Greek saved two set points and secured a break-back point of his own but dumped a shot into the net at the end of the longest rally of the set as Zverev held on.
Tsitsipas' shoulders visibly sagged as he offered up break point after break point at 1-1 in the second set.
When he dragged a shot long to end a game which had lasted over 15 minutes, his opponent was now firmly in the ascendancy and proved it by consolidating the break comfortably.
The Greek rallied to hold his next service games but struggled to challenge on the Zverev serve.
Zverev, who reached the French Open final on a previous visit to Paris this year, ruthlessly served out to win and keep alive his hopes of claiming a second ATP 1000-level trophy of the season.
'One of the best players'
Former world number four Rune, the 13th seed in Paris, needed just one break of serve as he took the opener against De Minaur.
In the second set, the Australian started to open up on his groundstrokes, producing several stunning winners off both wings that ignited the capacity crowd.
The dogged Rune finally relented when serving at 4-5, offering up three set points to De Minaur who duly converted with a well-constructed point in which he dragged the 21-year-old all over the court before dispatching an easy volley at the net.
The Australian's first serve gradually deserted him in the decider and Rune capitalised by breaking in the fifth game, but De Minaur struck immediately back to level.
A huge net cord that clipped the line on the right side of the court for Rune gave him a 0-15 lead and he took full advantage, breaking to lead 6-5 before consolidating to win the match.
"Sascha (Zverev) and I had a great match in Paris, where he took it in five. I beat him one time, he took me last time," Rune said of facing Zverev who came out on top when the pair met in a five-set clash in the last 16 of the French Open this year.
"He is one of the best players this year, so I will have to be very well prepared."
With the result, both Rune and De Minaur still have a chance of reaching the Tour Finals in Turin, which run November 10-17.
Later, Frenchman Ugo Humbert, who downed world number two Carlos Alcaraz in the last 16, defeated Australia's Jordan Thompson.
Russian Karen Khachanov plays last year's beaten finalist Grigor Dimitrov of Bulgaria in the final quarter-final.