Upon accepting the award at the FIFA Ballon d'Or Gala 2013 in Zurich, Sundhage – sporting a sparkling shirt reading "Sweden in 2013" – thanked staff and US players before breaking into an a cappella version of Bob Dylan's If Not for You (see video below).
"I wanted to surprise people and at the same time show that I'm the same old Pia," the 52-year-old Sundhage told the Expressen newspaper following the ceremony.
"It feels great to win this award and it was moving to see and meet several of the American players. But now it's time to move on because we have a European championship to host this summer."
Sundhage took over as coach of the US women's team in 2007, leading the team to Olympic gold in Beijing in 2008 less than a year later with a victory over Brazil.
After settling for a hard-fought silver in the 2011 World Cup following a loss to Japan on penalties, Sundhage's women mounted an impressive Olympic campaign in London, avenging their World Cup loss to Japan to once again claim gold.
Sundhage completed her tenure as US coach with an 88-6-10 record before agreeing in early September to take over as coach of the Swedish women's national team, where she starred as a player during a nearly 20-year career, scoring 71 goals in 146 appearances.
She is now preparing her squad for the 2013 European championships, which will take place in Sweden.
Monday's FIFA Ballon d'Or Gala also saw Barcelona star Lionel Messi win an
unprecedented fourth consecutive player of the year award, while the United States' Abby Wambach was named the best women's player of 2012.
Meanwhile, Spain's Vicente del Bosque was named men's coach of the year.