Taken just scant weeks prior to the October 20 local elections, the poll showed that 44 percent of eligible Tallinn voters would support Savisaar continuing in his job, a drop of four percentage points from August.
Kross emerged in September as the most popular opposition mayoral candidate. In August, he was fourth overall with 6 percent, but has now doubled that figure.
Third most popular is Social Democrat Andres Anvelt, backed by 9 percent, the same as in August.
Reform's Valdo Randpere lost support during the month, down to 7 percent from 12 percent.
Conservative People's Party leader Mart Helme stayed at 4 percent.
Aivar Voog of Emor said the change in Kross's popularity stemmed from IRL's campaign.
"The fact that they succeeded in embroiling the Center Party in debate worked in their favor. Center is now mainly quoting IRL and it seems that the media debate is taking place between Center and IRL."
One in three Estonian voters and nearly one in two Tallinners plan to vote for Center at local elections, the Emor poll revealed.
Center holds 31 percent support nationwide, followed by the Social Democrats with 16 percent, Reform with 13 percent and IRL with 9 percent.