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The England star showed compsure beyond his years to put Dortmund back in front in the 52nd minute, firing home his third goal of the season after collecting a pass from Youssoufa Moukoko and baffling the home defence to creat space for his shot.
There had been half-chances at either end before Dortmund took the lead in the 21st munute through Julian Brandt, who was found unmarked by Donyell Malen who had darted down the left before producing a cross Brandt converted through Kevin Trapp's legs.
Frankfurt leveled within five minutes, though, when Daichi Kamada fired into the bottom corner from the edge of the box.
It remained a frenetic encounter until the interval, but neither side was able to add to the scoreline, and even after Bellingham had put Dortmund back in front, the result was far from guaranteed.
Eintracht responded well, producing wave after wave of attacks. Kolo Muani was denied by an inspired Gregor Kobel a number of times, while Jesper Lindstrom saw his near-post flick clawed away and Mario Gotze had a venomous shot cleared off the line by Nico Schlotterbeck.
Dortmund breathed a sigh of relief at the final whistle, claiming the points to move into third spot on the Bundesliga table after Bayern Munich's earlier thrashing on Mainz had seen it return to the top. Eintracht sits in fifth in an increasingly right top six, with RB Leipzig holding sixth spot after its 2-0 win over Leverkusen.
Second-placed Union Berlin can regain top spot with a win on Monday (AEDT) against Borussia Moenchengladbach and Freiburg could push Dortmund back into fourth with victory at struggling Schalke on the same day.