Two goals from Sergei Terehhov proved the difference in these two sides.
His strikes came in the second half after a nervous first sesson from both teams who seemed unwilling to commit to attack.
Terehhov cut inside from the left to drive across the face of goal and into the net in the 49th minute and produced a weaving run in the 77th to beat three defenders and hit a low shot on the run into the net.
Substitute Formenka inspired a rally by the home side with a headed goal but Estonia hung on for the win.
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