Nils Petersen added the second to leave struggling Hamburg without a point or goal to their credit after two games of the new season and their coach Thorsten Fink under mounting pressure.
Hapless Hoffenheim had two players sent off, including substitute Sejad Salihovic four minutes after coming on, as they crashed to a 4-0 home defeat against promoted Eintracht Frankfurt, who have won both of their opening games.
Jefferson Farfan provided the assists for all three of Schalke 04's goals in their 3-1 win over Augsburg and title holders Borussia Dortmund drew 1-1 at Nuremberg.
Hamburg appear to be in for a long, hard season after a error-strewn performance at Bremen, where only goalkeeper Rene Adler kept the score respectable.
Both penalties were needlessly given away and Bremen's second came from one of several mistakes by Czech international midfielder Petr Jiracek.
Bremen, who have three points, won their first penalty in the 42nd minute for a clumsy challenge by Jeffrey Bruma on fellow Dutchman Eljero Elia.
Hunt sent the penalty to Adler's right but the goalkeeper made a brilliant save.
Hunt chose the same corner on his second attempt in the 52nd minute after Dennis Aogo fouled Petersen but this time hit it with more power and Adler, despite again going the right way, had no chance.
Bremen's second came after the disappointing Jiracek lost possession to Clemens Fritz inside his own half, the ball was laid off to Hunt and he found Petersen, who slotted the ball under Adler.
Adler denied Austrian pair Zlatko Junuzovic and Marko Arnautovic and made another superb save from Hunt late in the game.
Frankfurt took control of their game in a four-minute spell before halftime when Alexander Meier's low 25-metre drive was deflected in off a defender and Pirmin Schwegler scored with a viciously swerving shot from 30 metres.
It got worse for Hoffenheim, who have lost both opening games, as Salihovic came on in the 66th minute, was booked twice in four minutes and sent off.
He was followed three minutes later by Stephan Schrock, also for a second bookable offence. Meier made it 3-0 from a penalty and Martin Lanig added a fourth for the rampant visitors.
Poland midfielder Jakub Blaszczykowski scored five minutes before half-time to rescue a point for champions Dortmund, scoring from a rebound after Ivan Perisic's shot hit the underside of the crossbar.
Nuremberg had taken the lead nine minutes earlier when Czech forward Tomas Pekhart rose above the defence at the far post to score with a downward header from a corner.
Peru forward Farfan made an instant impact for Schalke on his return from injury as he provided the corner for Kyriakos Papadopoulos to head the opener after 33 minutes.
He also set Jermaine Jones on his way for an individual goal at the start of the second half and crossed for Dutchman Klaas Jan Huntelaar to head the third in the 72nd minute, his second goal in two games this season. Torsten Oehrl replied for pointless Augsburg.
Gonzalo Castro and Philipp Wollscheid gave Bayer Leverkusen a 2-0 win over Freiburg while top flight new boys Fortuna Dusseldorf contested a 0-0 draw with Borussia Monchengladbach elsewhere in Bundesliga action.
- Nils Petersen