Schalke booked a semi-final clash with Premier League giants Manchester United last Wednesday when they beat holders Inter Milan 2-1 at home to win their quarter-final clash after shocking the Italians 5-2 at the San Siro.
The Royal Blues now face Sir Alex Ferguson's United side on Tuesday, April 26 at the Veltins Arena in the semi-final first leg, but they had to fight back to share the points in the Bundesliga at mid-table Bremen.
"We could have won. In the second half we had some great chances, but I am very pleased with the way the team played," said coach Ralf Rangnick. "We showed plenty of energy in our performance after Wednesday's match against Inter Milan."
Bremen went ahead when striker Sandro Wagner was fouled in the penalty area and the 23-year-old netted the rebound after his 59th-minute spot-kick was saved.
But the Royal Blues immediately produced the perfect response when veteran Spain striker Raul fired in a cross from the sidelines that Brazil striker Edu blasted home with a bullet header on 63 minutes. The result leaves both teams in mid-table.
Earlier, a late equaliser by VfL Wolfsburg secured a 2-2 draw at home to St Pauli to give the 2009 Bundesliga champions a fighting chance of escaping the relegation zone.
Wolfsburg, coached by Felix Magath, who led them to the title only two years ago, are third from bottom and four points from safety with four games left before the season finishes on May 14.
After fellow relegation candidates St Pauli took a late 2-1 lead, a header from Czech midfielder Jan Polak with a minute left gave Wolves a crucial point.
Wolfsburg sacked ex-England manager Steve McClaren in February with the side sliding towards the relegation zone, allowing Magath to return after he in turn was shown the door by Schalke.
"I am satisfied with the result, but obviously not with the game," said Magath. "Once again, we have shown that we lack the things you need in a relegation fight. We lacked both the team spirit and the will to win this game."
The last two in the Bundesliga are relegated automatically, but the side third from bottom faces a play-off against the side third from top in the second division for the right to play in Germany's top flight next season.
With second-placed Bayer Leverkusen taking on defending champions Bayern Munich, who are fourth, on Sunday, just after leaders Borussia Dortmund play Freiburg, third-placed Hanover 96 were held to a goalless draw by Hamburg.
Hanover are on course to go into the play-off for a Champions League place, but they cannot now catch second-placed Leverkusen, who are 13 points ahead.
Dortmund remain on course for their first league title since 2002 as they enjoy a five-point lead over Leverkusen.
Stuttgart pulled away from the relegation zone with a 3-1 win at Cologne to put four points between themselves and the bottom three.
Hoffenheim moved up to ninth as Brazilian teenager Roberto Firmino scored his first goal for the club with a 78th-minute strike after being set up by ex-Liverpool forward Ryan Babel to earn a 1-0 win over Eintracht Frankfurt.