Zverev downs Tsitsipas to book place in semis of Paris Masters
The world number three -- the highest-ranked player left in the draw -- will face either 13th seed Holger Rune or ninth seed Alex de Minaur in Saturday's semi-final.
The 16th meeting between the 27-year-old German and 26-year-old 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."
But 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 Greek world number 11 of reaching the end-of-year ATP Finals this month -- having won the showpiece event in 2019.
Both players started cautiously with Tsitsipas double-faulting in the first game to give Zverev a chance at 30-30, before hitting an excellent drop shot to set up game point.
In reply, Zverev landed two shots in the tramlines to give Tsitsipas a 0-30 advantage on his serve before finding his rhythm.
Tsitsipas started the fourth game with a whipped forehand passing shot, but the 198cm-German showcased the sheer power of his groundstrokes and serve to hold.
Zverev and Tsitsipas both found their range on service as consecutives games were held to love to make it 4-3, and 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 failed to convert 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 claim a straight-sets win and keep alive his hopes of claiming a second ATP 1000-level trophy of the season.
Later, Frenchman Ugo Humbert, who downed world number two Carlos Alcaraz in the last round, takes on Australia's Jordan Thompson.
Rune of Denmark faces up against Australian De Minaur and Russian Karen Khachanov plays last year's beaten finalist eighth-seed Bulgarian Grigor Dimitrov in the other quarter-finals.