The second-seeded Roberto Bautista Agut will meet Canada's Felix Auger-Aliassime in the other semifinal.
Russia's Andrey Rublev edged closer to a maiden appearance in the ATP Finals on Saturday when he defeated fellow London season-finale hopeful Denis Shapovalov to reach the Saint Petersburg final.
"It's a good win".
"Obviously I'm happy to beat a player like this today".
Zverev is looking for his first title of the year and his third in his native Germany following victories at the clay-court Munich tournament in 2017 and 2018.
"I've practiced with him many times back home. It's going to be a great battle", said Auger-Aliassime, who trails their ATP Head2Head series 0-2.
Auger-Aliassime, seeded third at the ATP 250 indoor hardcourt event, converted five of his six break point chances and won 68 per cent of his service points, compared to 42 per cent for Albot. The 20-year-old Canadian has played the last nine games of 3-All in the first game and recorded his 20th win in 2020 against 14 losses.
"I think in the first set I played one of the best sets of my career".
"In my mind I knew it was goint to be a hard match", said Auger-Aliassime.
Auger-Aliassime easily lost the second set but then started the third set with a 3-0 lead and held on to his serve the rest of the decider to seal the win.
"I have got to do a better job of keeping my focus until the end of a match".
Things got a little more hard in the second set.