Eintracht's first season in the top flight for 28 years was promising enough until the 82nd minute, when Zlatko Junuzovic put the visitors in front.
The goal, which came from a speculative long ball forward, silenced the Braunschweig fans who had been dreaming of a better Bundesliga debut, which their side had probably deserved.
Back in the big time for the first time since 1985, Eintracht needed a little time to get used to their new surroundings.
Fortunately for them, they came up against a Bremen side who were willing to give them that time and who were pretty nervous themselves after being knocked out of the DFB-Pokal a week ago.
The first half was therefore spent largely in the midfield with neither side carving out any chances.
Eintracht discovered more courage in the second half and went close to breaking the deadlock in the 64th minute when Ken Reichel's shot was tipped onto the crossbar by Sebastian Mielitz.
Soon after, Ermin Bicakcic only just missed the target with an overhead kick as the home team increased the pressure.
On a rare break, Aaron Hunt saw his shot parried by Marjan Petkovic with Nils Petersen sending the rebound into the side-netting from a tight angle.
Bremen then struck with a goal out of the blue which they themselves had not even expected.
Sebastian Prodl's long clearance out of defence turned into an assist for Junuzovic, who let the ball pass him on the left before sweeping it high inside the near post.
The Eintracht Stadion fell silent with only a pocket of fans dressed in green celebrating an unlikely lead.
And just to typify Eintracht's day, Jan Hochscheidt saw his shot cleared off the line by Luca Caldirola in the 88th minute as the league newcomers were given a bitter baptism in the Bundesliga.