The strength-sapping match on a snowy pitch had a dramatic finale as Serbia thought they had won the it with the last kick when the ball trickled over the Estonian goal-line, only for the referee to disallow the goal for offside.
An opportunist first-half goal by striker Marko Pantelic on a barely playable surface had given Serbia the lead before Konstantin Vassiljev equalised in the 84th minute with a low free-kick which squeezed under Brkic's body into the net.
Having dominated the opening half in heavy snow, Serbia were on the back foot after the interval and were punished after missing two good chances.
Estonia keeper Sergei Pareiko denied Milan Jovanovic and Zoran Tosic before Vassiljev's free-kick from 30 metres somehow found its way past the wall and under Brkic.
Serbia had two goals disallowed for offside, the first in the opening minute and crucially in the dying moments, when the referee at first appeared to let it stand and then changed his decision after consulting his linesman.
It was a disappointing end for the 32-year-old Pantelic, who made the most of his second chance with the national team after he was dropped following a poor 2010 World Cup.
Having been recalled because of mounting injuries up front, Pantelic netted the equaliser in Friday's 2-1 home win over Northern Ireland on his return and was a handful for the Estonian back four.
Serbia's defence looked stronger with Nemanja Vidic back after missing the Northern Ireland game with a calf injury, but with the midfield running out of steam in the second half, the visitors paid the price for sitting back on their lead.
The result leaves the Serbs locked together on eight points wth Slovenia, who drew 0-0 in Northern Ireland. Italy, with a game in hand on both, lead the way on 13 points while Estonia (seven) and Northern Ireland (six) are still in the hunt for second place.
