Champions VfL Wolfsburg beat third-placed Schalke 04 2-1 to end a 12-match winless run in all competitions, with Grafite scoring both their goals in a six-minute second-half spell.
Bottom club Hertha Berlin won 3-0 at fellow strugglers Freiburg.
Leverkusen, who have 49 points, stayed unbeaten after 23 games and went top on goal difference from Bayern Munich, who drew 1-1 at relegation-threatened Nuremberg on Saturday.
Leverkusen appeared set for a win when Toni Kroos put them 2-1 ahead in the 57th minute but Per Mertesacker snatched an equaliser for Bremen in the second minute of stoppage time.
Schalke dropped four points behind the leading pair after losing an eight-match unbeaten run.
The leaders went ahead after half an hour when Switzerland striker Eren Derdiyok scored from a free kick, sending a superb right-foot shot over the wall and into the top right-hand corner for his 11th goal of the season.
But sixth-placed Werder equalised four minutes later thanks to a blunder from Leverkusen goalkeeper Rene Adler who failed to hold an easy-looking Naldo free-kick, allowing Peru striker Claudio Pizarro to tap the ball home for his 10th of the season.
The game fell away after the break until Kroos collected Tranquillo Barnetta's pass and scored with a vicious, swerving shot from around 30 metres.
Leverkusen looked set to go two points clear until Mertesacker headed in from Mesut Ozil's cross in almost the last move of the game.
Schalke, whose coach Felix Magath led Wolfsburg to the title last season, went ahead with a Kevin Kuranyi header from Ivan Rakitic's corner after half an hour against the run of play.
Brazilian striker Grafite, last season's topscorer, headed 12th-placed Wolfsburg level in the 71st minute and won the game with a clever flicked goal from Schaefer's cross six minutes later.
Hertha stayed bottom with 15 points but closed the gap on Nuremberg and Hanover to only two points and Freiburg to four after their third win of the season.
Colombia striker Adrian Ramos opened the scoring before Brazilian Cicero scored either side of half-time.
