The goalkeeper was arguably at fault for all three of Hamburg's goals as Freiburg slipped deeper into the relegation mire.
Baumann's difficulties began on 37 minutes when a moment of madness saw him race off his line and misjudge a long ball from the back of the Hamburg defence, allowing Maximilian Beister to slot into an empty net.
Things got worse for Baumann two minutes into the second half as he attempted to bring the ball back into his own area but saw Pierre-Michel Lasogga nip in and double Hamburg's advantage
A miserable performance was completed when Baumann spilled a Beister shot into the path of Rafael van der Vaart, who applied a cool finish to find the net.
Hamburg were therefore able to celebrate only their second win of the season, while Freiburg continue to seek a first victory.
In the day's other game, Eintracht Frankfurt's five-match unbeaten run was brought to an abrupt end as a rampant Borussia Monchengladbach ran out 4-1 winners at Borussia Park.
Early goals for Juan Arango and Oscar Wendt sandwiched Stefan Aigner's equaliser for Frankfurt.
Things got better for Lucien Favre's side in the second half, when a dominant performance culminated in goals from Patrick Herrmann and Raffael.
Borussia's win was their fifth in succession on home soil and lifted them up to fourth in the table.