The Czech took three hours, 15 minutes to defeat Wawrinka in four sets, 6-3, 6-4, 3-6, 7-6 (5).
The pair faced each other on the court a day after the longest Davis Cup match ever on Saturday, a doubles face-off that took seven hours and two minutes.
Berdych and Lukas Rosol beat Wawrinka and Marco Chiudinelli 6-4, 5-7, 6-4, 6-7 (3/7), 24-22.
The marathon match surpassed the previous record when John McEnroe needed 6 hours and 22 minutes to beat Mats Wilander 9-7, 6-2, 15-17, 3-6, 8-6 in the tie between the United States and Sweden in 1982.
The previous longest doubles match in Davis Cup was 6 hours 20 minutes which occurred in 2002 when Lucas Arnold and David Nalbandian of Argentina beat Russia's Yevgeny Kafelnikov and Marat Safin 6-4, 6-4, 5-7, 3-6, 19-17.
The defending champion Czechs now play in the quarterfinals against Kazakhstan in April.
Switzerland had to play without top player Roger Federer, who bowed out of the tournament.
The weekend losses for Wawrinka come on the heels of his heartbreak 12-10 defeat to Australian Open champion Novak Djokovic in the fifth set of the fourth round of the Australian Open last month, after five hours, two minutes.
Back on court after both played in an epic 7 hours, 1 minute doubles match on Saturday, Czech No. 1 Berdych beat Swiss team leader Wawrinka 6-3, 6-4, 3-6, 7-6 (5) in the first of the reverse singles rubbers.
Sunday's match took three hours, 15 minutes - lasting less than half the time of the longest match in Davis Cup history. The defending champion Czechs earned a home quarterfinal against Kazakhstan in April.
Wawrinka extended his run of hard-luck losses in 2013, which began against Australian Open champion Novak Djokovic when he lost 12-10 in the fifth set after 5 hours, 2 minutes.