Tipsarevic opened the series by beating Filip Prpic 6-3, 6-3, 6-4 and Troicki defeated Michael Ryderstedt 6-4, 6-3, 5-7, 6-3 to put the Serbs one win away from advancing.
A win in Saturday's doubles would send Serbia into the cup quarterfinals April 6-8 against either the Czech Republic or Italy.
Sunday's schedule calls for reverse singles with Tipsarevic taking on Ryderstedt and Troicki meeting Prpic.
Tipsarevic used just more than 2 hours in getting by Prpic. He finished four of his five break-point chances while saving the five chances Prpic managed.
Troicki was in control after seeing just one break point in the first two sets but Ryderstedt used a late third-set break to extend the match. Troicki then took the advantage with a break in the sixth game of the fourth set and served out for the win.