Serbia is playing without its three highest ranking players, including world No. 2 Novak Djokovic, and the Swiss took advantage of the situation. Federer rolled to a 6-4, 5-7, 6-2 victory over Ilija Bozoljac and Wawrinka beat Dusan Lajovic 6-4, 4-6, 6-1, 7-6 (9-7).
Federer faced a set point in the second set against Bozoljac but won five straight games to take the set and then allowed the Serb just 13 points in the third set.
Federer won 78 percent of the points on serve and saw just two break points. He had 38 winners against 14 unforced errors.
Wawrinka, coming off Sunday's Australian Open title match win over Rafael Nadal, had more trouble with Lajovic, losing the second set and then fighting off two set points in the fourth-set tiebreaker.
Wawrinka seemed to be having trouble with his right arm in the latter stages of the match before Lajovic missed an overhead on match point.
Switzerland has three chances to claim the series win. The first opportunity comes Saturday when the Swiss doubles team of Michael Lammer and Marco Chiudinelli takes on Filip Krajinovic and Nenad Zimonjic.
Federer goes against Lajovic in the first singles match Sunday and Wawrinka is scheduled to take on Bozoljac in the second.
The winner of the Swiss-Serb series moves into the Davis Cup quarterfinals April 4-6 against either Kazakhstan or Belgium. The Kazaks are up 2-0 in that first-round series.