
Carlos Grossmueller put Schalke ahead in the 14th, with Naldo levelling 20 minutes later.
Munich, who are at Borussia Dortmund on Sunday, have a big lead with 26 points. Bremen are on 21, followed by SV Hamburg (who visit lowly Duisburg Sunday) and SC Karlsruhe, who are both on 20. Schalke are fifth with 18 points.
Champions Stuttgart, meanwhile, got a vital 1-0 over Bayer Leverkusen to move away from the lowlands into 12th place.
Stuttgart beat Schalke and Bremen for the 2007 trophy, with Schalke and Bremen high in the standings again this season.
Schalke went on top early on from Grossmueller's first league goal, a well-executed curling free-kick in the 14th minute.
But Bremen battled back with Boubacar Sanogo close in the 23rd with a volley. The equalizer came another 11 minutes later in the 34th when Naldo headed home a freekick from Tim Borowski.
Bremen could have stolen a vital away win but Sanogo incredibly volleyed wide from point-blank range after a fine right-wing cross from Germany midfielder Torsten Frings.
"We played well after a slow start and even had chances to win in the second half. But Schalke had their chances as well so the draw is a deserved result. We got a point and are satisfied," said Frings.
Schlake's Christian Pander said: "We are not satisfied. We played well but once again we missed chances and weren't lucky either. We are not looking at Munich, but have claimed important points against a rival high up in the standings."
Stuttgart made a first step out of a deep crisis with the lucky win over Leverkusen, their first in the league in three matches and overall in five matches.
Sergej Barbarez and Stefan Kiessling came close for the visitors but Andreas Beck soothed Stuttgart's nerves with the 72nd-minute winner from a penalty-area scramble.
Elsewhere, Arminia Bielefeld beat winless bottom club Energie Cottbus 1-0, Hertha Berlin ended a mini-slump with a 2-0 win over drop-zone club VfL Bochum, and Rostock held the surprise team of Karlsruhe to their second straight 0-0 draw.
VfL Wolfsburg, meanwhile, beat struggling cup winners Nuremberg 3-1, with Ashkan Dejagah the best man on the pitch a few weeks after the Iran-born player caused a huge controversy for not playing with Germany's under-21 team in Israel.
Dejagah set up Grafite for Wolfsburg's second in the 35th and scored the third himself in the 67th to clinch victory. Wolfsburg's first came from an own goal by Angelos Charisteas and Nuremberg got on the scoreboard with a 54th-minute penalty.
On Friday, Eintracht Frankfurt and Hanover 96 played to a goalless draw.
DPA