The fifth-seeded Berdych, who won on his Bercy debut in 2005, is the sixth player to secure his place in the November 9-16 elite eight-man event in London.
After losing the opening set tiebreak, Berdych found his range on serve to level and recovered from a break down in the third set before breaking the 14th seeded Anderson's serve decisively in the ninth game.
Berdych will next face either Swiss great Roger Federer, seeded second, or Canadian Milos Raonic, the seventh seed.
In the other half of the draw world number one Novak Djokovic faces Andy Murray while Kei Nishikori is up against Spain's David Ferrer.
The Race to London: Points
1. Novak Djokovic 9190 - qualified
2. Roger Federer 8700 - qualified
3. Rafael Nadal 6835 - withdrew
4. Stan Wawrinka 4895 - qualified
5. Andy Murray 4475 - qualified
6. Tomas Berdych 4465 – qualified
7. Kei Nishikori 4445
8. Marin Cilic 4150 - qualified
9. David Ferrer 4045
10. Milos Raonic 4020
Image: Tomas Berdych
Photograph: Dean Mouhtaropoulos/Getty Images
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