The Spanish striker, who joined Dortmund from Barcelona in the offseason, scored the winner to give Lucien Favre's men three vital points in the league.
The game's only goal came in the 28th minute of the first half on Friday when the German team was handed a penalty.
The 30-year-old center back is the third new arrival since Unai Emery replaced Arsene Wenger as manager in May, joining full-back Stephan Lichtsteiner and goalkeeper Bernd Leno.
Frankfurt, which had twice come from behind to pull level, is two points behind Bayer Leverkusen, which occupies the last Champions League qualification spot.
Athletic Bilbao are scheduled to next face Marseille, while Borussia Dortmund will take on Austrian side Salzburg.
Arsenal powered past Ostersund 3-0, Atletico Madrid thrashed Copenhagen 4-1 and Italian league leader Napoli slipped to a surprise 3-1 home defeat against Leipzig.
Reus was handed the captain's armband 259 days after the German forward sustained a cruciate ligament injury in the German Cup final.
Aubameyang's signature might be one of the key reasons for German International Mesut Ozil to pen a new deal with the Gunners as his contract runs out at the end of the season.
Arsenal have set their eyes on three targets this winter which include Argentine Cristian Pavon from Boca Junior, Malcolm from Bordeaux and Aubameyang from Borussia Dortmund.
The German Clasico saw the league leaders Bayern Munich knockout arch-rivals Borussia Dortmund as Muller and Boateng shined in goal.
In other ties, Scottish club Celtic F.C will host Russian club Zenit St Petersburg, Napoli will play RB Leipzig, Ludogorets will take on seven-time European champions AC Milan.
Stoeger was sacked as Cologne coach the previous Sunday after his side failed to win any of its opening 14 Bundesliga games of the season.
Madrid had already guaranteed second place behind Group H winner Tottenham, which defeated APOEL 3-0 at Wembley Stadium to reach 16 points.
The hosts let a four-goal lead slip away after Schalke ran riot after half-time to salvage a draw in the dying minutes of a thriller match.
The club does not give an indication of what led to the sanction for the Gabon forward.
Dortmund, which reached the final in 2013, started well against a side that hadn't scored in its previous six games but then stagnated as APOEL organized.
Counterpart Carlo Ancelotti was left pondering how his side lost after 23 efforts at goal.
Barcelona have mentioned that Dembele's contract will have a buyout clause of 400 million euros ($472 million).
Pulisic scored Dortmund's first league goal of the season after good work by Mario Goetze, who was making his first Bundesliga start since December after an illness.
Paulinho's contract is set to include a buyout clause worth up to 120 million euros ($142 million).
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