Last season's surprise runners-up Stuttgart, without injured Germany forward Deniz Undav, hit the bar twice in Sunday's match through Ermedin Demirovic.
The Bosnia striker also saw his poor penalty easily saved by Kevin Trapp after Angelo Stiller had been tripped by Hugo Larsson.
Jeff Chabot then thought he had finally put the hosts into the lead but his header from a free-kick was ruled out for offside.
Frankfurt's much-vaunted attack, including Bundesliga second top scorer and assist king Marmoush, struggled early on after the Egyptian missed a good chance.
But after Stuttgart's three big opportunities, Marmoush's corner was superbly headed in by strike partner Hugo Ekitiké just before the interval.
Nathaniel Brown's tap-in after Ansgar Knauff's run and deflected cross made it 2-0 before Marmoush's latest free-kick goal after strikes in the 1-0 Europa League win over Slavia Prague on Thursday and last weekend's 7-2 thrashing of Bochum.
Josha Vagnoman and Nick Woltemade then slashed the deficit and Chris Führich thought he had netted an incredible equaliser in stoppage time, only for video review to chalk it off for offside.
"That would have been very, very annoying if we had led 3-0 and not have won that," Frankfurt's Trapp told DAZN. "You can't stop playing just because you are 3-0 up."
Stuttgart sit 11th while Frankfurt are three points clear in third, just a point behind second-placed RB Leipzig.
Hoffenheim earlier lifted themselves out of the Bundesliga relegation play-off spot into fourth-bottom with a 0-0 draw at Augsburg.
The mid-table hosts dominated the first half and had several chances. Hoffenheim improved after the break but Augsburg's Arne Maier and Steve Mounié then arguably had the best opportunities of the second period.
The point may not be enough for Hoffenheim coach Pellegrino Matarazzo to keep his job before the next game against Leipzig on November 23.
"We will certainly talk to him," sporting director Andreas Schicker told reporters. "The number of points we have is not what we wanted."
Wolfsburg moved away from the drop zone after their third away win of the season in a 3-1 victory at Heidenheim in the final game of matchday 10 before the international break.
On Saturday, Bayern Munich extended their lead at the top to five points with a 1-0 win over promoted St Pauli.
