Thombare defeated Dianne Hollands 6-1, 6-4 in the first singles.
New Zealand levelled the tie when Marina Erakovic beat Ankita Raina 6-1, 6-2.
Thombare then teamed up with the experienced Sania to get past Erakovic and Abigail Guthrie 7-5, 6-1, giving India their third win a row.
India blanked Iran and Pakistan earlier in the competition.
They next play Group A winners Hong Kong.