Gladbach moves to top four of table
Juan Arango got Gladbach off the mark with a free kick in the 11th, only for Stefan Aigner to equalize four minutes later when Marc-Andre ter Stegen was fortunate that advantage was played after a clear foul on Vaclav Kadlec.
Had referee Felix Zwayer awarded the penalty, he would have been forced to send the goalkeeper off, but he awarded the score after Aigner fired home the loose ball from close range.
Oscar Wendt restored the home side's advantage three minutes later with a fine strike inside the near post after playing a one-two with Raffael.
Patrick Herrmann effectively decided the game, shooting inside the bottom left corner on the hour, and then setting-up Raffael's goal six minutes later after a well-worked move involving Julian Korb.
''It was OK, it was good,'' said Gladbach coach Lucien Favre, who played down his side's chances of ending the season in fourth. ''There are many other teams who will be challenging too. You have Schalke, you have Wolfsburg, it's very close. The team in 14th (Frankfurt) has national team players. We have to stay grounded.''
Baumann misjudged a long ball from Milan Badelj and failed to clear after emerging outside the penalty area, allowing Maximilian Beister to open the scoring in the 37th minute.
Two minutes after the interval, Baumann again found himself outside the penalty area for Rafael van der Vaart's hopeful punt forward. The goalkeeper waited, then fumbled and Pierre-Michel Lasogga swooped to fire into the empty net.
Baumann also spilled Beister's straightforward shot to let Van der Vaart score in the 63rd.
''The actions didn't work out as I'd imagined they would. You have to cope with it, we're human,'' Bauman said. ''My confidence isn't affected. Sure, it's a (bad) situation but ... we have to stay calm, shouldn't go crazy.''
Baumann redeemed himself somewhat with a good save in a one-on-one with Ivo Ilicevic late on, before both Freiburg and Hamburg players consoled the goalkeeper after the match.
''They told me they were sorry for me. Lasogga and Beister are good sorts. It was nice of them,'' Baumann said of his former Germany under-21 teammates.
Freiburg coach Christian Streich said he'd speak with the goalkeeper on Monday.
''I've experienced many things in the last few weeks that I've never before experienced in football,'' Streich said.
Freiburg remains second from bottom, one of two sides yet to win after 10 rounds of the Bundesliga. Hamburg climbs to 12th after two wins and two draws since Bert van Marwijk was appointed coach.
''We deserved to win. We created plenty of other chances to score,'' said Van Marwijk. ''Of course, we were lucky with the goals.''
On Saturday, league leader Bayern Munich was made to work hard for a 3-2 win over Hertha Berlin, while Borussia Dortmund and Bayer Leverkusen stayed one point behind with wins over Schalke and Augsburg, respectively.