A winning streak of twelve matches ended for Kontaveit after she had previously won the tournaments in Cluj-Napoca and Moscow.
In Group A, the Spaniard Paula Badosa has already been selected as the semi-finalist before the last group match on Monday.
The top seed Aryna Sabalenka (Belarus) and the Greek Maria Sakkari fight for the last ticket in a direct duel.
Bitter tears in Turin: Berrettini injury ensures Zverev victory