The 36-year-old Haas produced some inspirational tennis to frustrate Wawrinka.
Stanislas Wawrinka loses to Austrian qualifier Dominic Thiem 1-6 6-2 6-4 in second round.
Australian Open champion Wawrinka recovered from opening set loss to claim maiden Masters title.
Holder Djokovic resisted for one set before pain in his right wrist was just too much to bear.
Nadal thrashed Italy’s Andreas Seppi 6-1 6-3 while fourth seed Federer defeated Czech Lukas Rosol 6-4 6-1.
Like Switzerland, Italy and France also trailed 2-1 in their quarterfinals going into the final day.
Switzerland last reached a Davis Cup semi 11 years ago, when Federer lost a key five-setter against Australia’s Lleyton Hewitt.
Nadal looked more comfortable in the final and improved his record on clay to 298 wins and 21 losses, the best in the Open Era.
The Spaniard Rafael Nadal declined to talk about his back, focusing instead on the victory.
Federer beat Ilija Bozoljac in straight sets while Wawrinka, fresh from winning his maiden grand slam title at the Australian Open.
Exhausted after the Australian Open win over Rafael Nadal, Stanislas Wawrinka should still be too strong for the Serbian side.
Stanislas Wawrinka is as deserving a Grand Slam winner as any other, even his opponent.
The top seed was denied a 14th Grand Slam title by in-form Swiss star Stanislas Wawrinka.
Switzerland’s Stanislas Wawrinka claimed his first Grand Slam title in dramatic fashion on Sunday.
Wawrinka knocked out three-time Australian Open champion Novak Djokovic in the quarterfinals.