Hanover moved up to 54 points with four games left while Bayern, fourth with 52, host second-placed Bayer Leverkusen on Sunday needing a win to regain third place.
Dortmund and Leverkusen (61 points) appear certain to finish in the top two and take Germany's direct group stage places in the Champions League, leaving Bayern to scrap with Hanover for third spot and a place in the qualifying round.
A fourth-place finish would mean a place in the Europa League, which would be a huge indignity for Bayern especially with next season's Champions League final at their own Allianz Arena.
Hanover, who saw Mohammed Abdellaoue's effort cleared on the line after 15 minutes, had no trouble keeping Hamburg at bay but struggled to carve out scoring chances in a very physical game.
Both teams came agonisingly close late in the second half with Hanover's Didier Ya Konan firing just wide in the 76th minute and Hamburg midfielder Eljero Elia's shot seconds later cleared off the line.
"Our defence was very focused today and so we deserved to get the one point in the end," said Hanover coach Mirko Slomka.
"It was important to keep a clean sheet after we conceded eight goals in our last two away games."
Wagner saw his penalty saved by Manuel Neuer but snapped up the rebound.
Spaniard Raul twice came close to equalising but it was Brazilian Edu who snatched a point when he headed in four minutes later to lift Schalke to 40 points in 10th place.
Both teams are on 29 points with Wolfsburg in 16th place, the relegation playoff spot, on goal difference from St Pauli, who are 17th and in the danger zone.
Stuttgart , long stuck in the bottom places themselves, continued their timely recovery by scoring three goals in 12 minutes to beat hosts Cologne 3-1 and move up to 33 points, four clear of Wolfsburg.