Hunt sealed the three points for Hamburg after Bobby Wood broke the offside trap before squaring to the Germany global to tap in and end Hoffenheim's seven-match unbeaten run.
Despite possessing the league's best scorer in Pierre-Emerick Aubameyang, who has 25 goals, Dortmund coach Thomas Tuchel has seen his team waste a myriad of chances throughout the season, dropping points they now urgently need to grab back.
Muller was restricted to a jogging session on grass, but the Italian said: "They'll certainly be available against Real Madrid".
Borussia Dortmund's injury list is rather longer: Mario Götze, Erik Durm, André Schürrle, and Sebastian Rode are all certain absentees; Marcel Schmelzer, Marc Bartra, Łukasz Piszczek, Julian Weigl, Shinji Kagawa, and Marco Reus all face late fitness tests.
Bayern host Real next Wednesday in a mouth-watering Champions League quarter-final first-leg clash, while Dortmund host Monaco on Tuesday in their home-leg match.
"So on Saturday we will give it all we have", said Hummels. "We want to hurt Bayern", he told reporters.
Robert Lewandowski doubled the lead from a free-kick before Raphael Guerreiro reduced the deficit.
Second-placed Leipzig had captain Willi Orban sent off for a second yellow card on 88 minutes for a foul on Leverkusen's Germany forward Kevin Volland.
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Hoffenheim suffered a shock 2-1 loss at Hamburg SV with Aaron Hunt scoring twice for the hosts, to remain third on 51, a point ahead of Dortmund.
But Forsberg staged one last run down the wing and found Poulsen, who slid in to score off the post deep in stoppage time to lift Leipzig to 58 points. We were ultimately unable to take points from here.
"Now we're in a great position for our next game", he added with RB at home to fifth-placed Freiburg next Saturday.
Wolfsburg, the 2009 champions, are just one point above the bottom three after a 4-1 hammering away to mid-table Schalke, for whom Guido Burgstaller netted twice.
One player who will be back for Bayern this weekend is winger Douglas Costa after three weeks out with a knee problem.
Cologne lost 3-2 at home to local rivals and fellow European hopefuls Borussia Moenchengladbach.
Then 'Gladbach captain Lars Stindl struck the victor in the 80th to lift the side to eighth, a point behind Cologne in sixth.