Two penalties from Aaron Hunt did not appease the home fans, who vented their anger at yet another lacklustre performance and disappointing home result for the northern Germany side, who can forget about any lingering hope they had of qualifying for Europe next season.
Stephan Furstner and Thanos Petsos accounted for Furth's goals as they picked up their 15th point of the season, remaining 14 points adrift of safety with eight games of the season remaining.
The first chances fell Furth's way with Bernd Nehrig going closest, prompting the first round of whistles from the home fans.
The whistling intensified when Furstner went close, and not even a shot from Nils Petersen into the side-netting could save the home side from the chorus of disapproval which greeted the half-time whistle.
Fortunately for Bremen, they were given an immediate chance to win over the home fans when Hunt was fouled by Lasse Sobiech inside the penalty area.
Hunt stepped up to the spot and put Bremen ahead in the 47th minute.
Their lead lasted just eight minutes before Furstner ghosted in unmarked at the far post to convert Heinrich Schmidtgal's cross.
Coach Kramer said he wanted to see his side's pride in the face of what seems like inevitable relegation, and he got even more than he had bargained for when Petsos put them in front five minutes later.
His direct free-kick beat Sebastian Mielitz and, once again, prompted the boos to echo around the Weser Stadion.
Another penalty allowed Hunt to level matters in the 70th minute, but Bremen could not find a winner as they saw their advantage over the bottom three reduce to just six points, while they are now eight points away from the top six.