Frenchman Hugo Ekitiké stepped up in the absence of his strike partner on 18 minutes following a fine move, with Oscar Höjlund scoring in stoppage time to secure the points.
While Egypt's Marmoush looks set to join Manchester City, the future of Sahin looks unclear after a third defeat in a row since the mid-season break.
They lost 3-2 at home to champions Bayer Leverkusen last Friday and 4-2 at promoted Holstein Kiel in mid-week.
A wave of 'flu in the camp could partly excuse those defeats but a third on the trot - albeit at third-placed Frankfurt - will leave fans furious given all the ill players were back fit.
"Of course it brings questions and criticism. Of course we have made mistakes again. It is very disappointing," Dortmund sporting director Sebastian Kehl told DAZN ahead of the side visiting Bologna in the Champions League on Tuesday.
"We will stay with how things are, Nuri has our backing."
Captain Emre Can said: "It's not good enough. We played better in the second half, but none of that matters, we've got to win. The table doesn't lie."
Dortmund, Champions League runners-up last term under Edin Terzic, are 11 points behind Frankfurt in 10th.
Sahin's appointment to replace Terzic in June was as big a surprise as his predecessor's exit. The former Turkey international had been Terzic's assistant and won a Bundesliga title with Dortmund in 2011, but his only managerial experience was a short spell at Antalyaspor.
It could have been different for Sahin had Serhou Guirassy scored instead of heading against the post early on. They also dominated the second half and had three penalty appeals waved away.
Etikité started and finished the flowing move for 1-0 when he swept home for his ninth goal of the league season. He almost had a second when he fired just over and Höjlund made the points safe late on as Dortmund pushed forward.
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