Stako put Ukraine ahead of Monaco 2-0 following his 6-1, 6-7(3), 7-6(3), 6-3 win against Jean Lisnard.
In the opening rubber, Ilya Marchenko defeated Benjamin Balleret 3-6, 6-3, 6-1, 6-1.
Sergei Bubka and Denys Molchanov will aim to clinch the tie when they square off against G. Couillard and T. Oger on Saturday.