Raffael gave Gladbach the lead in the sixth minute, but Bremen did not give up and they got their reward two minutes from time when winter signing Obraniak opened his account for the club at just the right time.
The draw takes Bremen five points clear of the relegation zone while Gladbach failed to put fourth-placed Schalke under pressure and saw their hopes of qualifying for the Champions League suffer a setback.
Nils Petersen almost gave Bremen a flying start when he was denied by Marc-Andre ter Stegen in the first minute, but it was Gladbach who settled quicker and took the lead in the sixth minute.
Assani Lukimya gifted Raffael with possession, leaving him with just Raphael Wolf to beat, and the Brazilian made no mistake to score Gladbach's quickest goal of the season.
Another mistake from Lukimya nearly allowed Gladbach in for a second and Robin Dutt responded by removing him with Felix Kroos coming on after only 27 minutes.
Bremen had a chance to level when Petersen moved up a gear and raced through, using his strength to hold off Oscar Wendt before shooting straight at Ter Stegen.
It was nevertheless a warning that Bremen were going to fight for a point with Petersen leading the charge, also just before half-time when he intercepted a pass from Wendt, but failed to beat Ter Stegen from a tight angle.
Petersen missed Bremen's first chance of the second half when he sent Franco Di Santo's cross wide, but Bremen continued to hammer away at their visitors.
Dutt's men threw caution to the wind and almost conceded a second when Patrick Herrmann was denied by a fine reflex save from Wolf.
Gladbach started gaining more chances to increase their lead as Bremen commit more and more men forwards, and after riding their luck, the hosts earned their reward with just two minutes left on the clock.
Like the man he has been compared to since his arrival from Bordeaux, Obraniak emulated Johan Micoud to curl a free-kick over the wall and into the top corner to bring Bremen level.
Dutt's men still almost lost the game when Max Kruse brought another fine save out of Wolf in the dying seconds, but it would have been cruel on Bremen, who had fought back well in the second half.