After Germany enjoyed a 2-0 lead from Saturday, Andrea Petkovic continued the hosts domination with a straight-sets victory over Melanie Oudin early on Sunday which gave the Germans an unassailable 3-0 lead.
The 23-year-old Petkovic needed just one hour 18 minutes to beat 19-year-old Oudin 6-2, 6-3, while team-mate Sabine Lisicki blitzed her teenage opponent Christine McHale in 88 minutes for a 6-3, 6-4 victory.
And doubles pair Julia Goerges and Anna-Lena Groenefeld completed the rout when they bounced back from losing the first set to enjoy a 3-6, 6-3, 6-1 victory over Liezel Huber and Vania King.
"We have proved that we belong in the top tier and we led from the front," said Australian Open quarter-finalist Petkovic after the Germans success.
The United States had reached the Fed Cup final for the last two years but came to Stuttgart with an inexperienced squad.
The Americans were missing their three leading players, including both the Williams sisters - Serena and Venus - as well as Bethanie Mattek-Sands, ranked 41st in the world.
Germany will now compete in the top tier of the Fed Cup in 2012 and team coach Barbara Rittner, who was part of the Germany team led by Steffi Graf which won the title in 1987 and 1992, was delighted.
"We have a lot of quality in the team and they all encourage each other," said Rittner.
But Petkovic said her current career-high ranking of 19th in the world was both a blessing and a curse.
"This is a new situation for me. I've noticed already in Miami that the young players play their best tennis against me," admitted the 23-year-old, who will contest the WTA tournament in Stuttgart starting Monday.