Bremen had found some light between themselves and the relegation battle following their last-gasp 2-1 win over Hannover last week.
They took the lead through Franco Di Santo, who also netted in the win over Hannover, but the hosts had to settle for a point on this occasion with Leon Goretzka levelling for third-placed Schalke in the first half.
Bremen's tigerish attitude put them on top early on with Cedric Makiadi seeing his shot blocked among a clutch of white Schalke shirts.
The home side were ahead by the quarter-hour as Eljero Elia pounced on some slack defending from Tim Hoogland and played in former Chelsea man Di Santo who sneaked the ball over the line from the tightest of angles.
Fifteen minutes later Schalke drew level through 18-year-old midfielder Goretzka. The youngster anticipated the second ball from Bremen's clumsy defending and drilling home a sweet shot.
Moments later, Sebastian Prodl pulled off an important headed clearance from the goal-line to prevent the Royal Blues going ahead.
The second half played out with limited efforts on goal, the most notable of which was Zlatko Junuzovic's half-volley after 57 minutes which forced Ralf Fahrmann into a strong save.
But Bremen held on, content to make it four points from two games and further ease their relegation fears.