The Serbian won her second match from two round-robin clashes in the Bulgarian capital, defeating Australian Sam Stosur 6-2 5-7 6-2.
Ivanovic said on www.wtatennis.com: "I played a little bit of a loose game at the end of the second set and was rushing a little bit too much, but I managed to calm down and start fresh in the third set.
"I started the third set in the same manner as I started the match, so I was very happy about that."
Ivanovic still has work to do in her final group match against Russia's Elena Vesnina, who kept her hopes alive with a 6-2 4-6 6-0 win over home hope Tsvetana Pironkova.
With two defeats, Pironkova is out of contention ahead of her third match against Stosur, with the other three competing for the two spots available.
In the other group, Romanian top seed Simona Halep continued her perfect record with a thumping 6-1 6-1 victory over Elina Svitolina.
Halep was already assured of her spot in the last four, while the winner of Friday's clash between Anastasia Pavlyuchenkova and Alize Cornet will take second place.