An own goal from Berkay Dabanli gave the hosts the lead in the eighth minute and Eljero Elia ended a 3361-minute drought with a brace, but that was not enough to earn Bremen all three points.
Hiroshi Kiyotake and Josip Drmic got the visitors back on level terms from 2-0 down, and Adam Hlousek's 70th-minute equaliser ensured a 3-3 result for draw specialists Nuremberg, who have now taken a point from five of their seven league games this season.
Buoyed by their derby win against Hamburg last weekend, Bremen soon got at Nuremberg with the same verve, taking the lead in the eighth minute.
Santiago Garcia, a summer recruit from Palermo, sent in a low cross-shot which took a decisive deflection off Dabanli to beat Raphael Schafer inside his near post.
Bremen continued to attack, with Aaron Hunt's angled shot saved well by Schafer and Nils Petersen unable to scramble the rebound home.
A second goal was in the air, but the provider was a surprise as Elia scored his first Bundesliga goal since netting for Hamburg in 2010, sending the ball just beyond Schafer's reach into the top-right corner.
Bremen appeared to be cruising, but Nuremberg are not a side to be written off. Kiyotake hammered the ball into the roof of the net from close range on the stroke of half-time, and a recovery was on the cards.
Drmic was introduced at the start of the second half and he lashed a shot wide from the edge of the area as the visitors grew in confidence.
The 21-year-old Swiss striker's next touch was a goal as he was left unattended at the far post and wrong-footed Sebastian Mielitz to bring Nuremberg level.
Bremen sparked back into action, however. Just as Nuremberg thought they had cleared their lines, the ball fell to Elia 25 yards from goal, and he sent it straight back in off the left post to put the hosts back in front in the 66th minute.
But Nuremberg responded well again, Hlousek latching onto Kiyotake's pass to restore parity once more 20 minutes from time.
Tomas Pekhart directed a free header straight at Mielitz, who then made a fine one-handed save and saw Drmic's shot hit the crossbar as the Bavarians searched with more insistence for a winner. But, like in their six previous leaguegames, they failed to find it.