Bremen offered very little going forward, with Hertha regularly threatening to extend their lead as Schieber saw a powerful strike stopped by Raphael Wolf midway through the first half.
Their advantage should have been larger before the break, but Genki Haraguchi was guilty of wasting a great opportunity when he sent a free header wide of the target.
It appeared that the hosts were on their way to a comfortable victory in the early stages of the second half when Schieber capitalised on mayhem in the Bremen box to fire in his second of the afternoon.
However, the drama was far from over as the visitors hit back in the 53rd minute, with Assani Lukimya heading home from Zlatko Junuzovic's cross.
Schieber should have completed his hat-trick and restored Berlin's lead, but he could only glance a header wide from a promising position inside the box.
Bremen too had an opportunity to steal a win late on after breaking free of the home defence, but his low strike was impressively stopped by Kraft as both sides had to settle for the point.