Marmoush struck in the fourth minute of time added on after Bayern had failed to settle the match earlier and were caught out three times on the counter in Sunday's clash.
Dominant Bayern led from Kim Minjae in the 15th minute but Frankfurt hit back twice on the break. Marmosuh levelled in the 22nd and set up attacking partner Hugo Ekitike to make it 2-1 in the 35th.
Bayern's other centre back, Dayot Upamecano, restored parity at 2-2 three minutes later, and Michael Olise put Bayern ahead again eight minutes after the restart.
Yet Bundesliga top scorer Marmoush had the last laugh with a league-leading eighth goal of the season to provide another setback in Bayern's bid to regain the title from Bayer Leverkusen.
"We played great as a team. We were ruthless in front of goal on the few chances we got," Marmoush said.
"I try to be consistent. But I must also thank the team. It is a lot of fun with the team. We are like a family on the pitch."
Bayern forward Thomas Müller said: "We must win the game if you dominate in such a way. It wasn't clever in the end. We didn't win but I still have a very good feeling."
It was Bayern's third game without victory after they were held 1-1 by Leverkusen a week ago and then lost for the first time in the season in midweek, 1-0 at Aston Villa in the Champions League.
But they still remain top, ahead on goal difference from RB Leipzig, who won 1-0 at Heidenheim earlier on Sunday.
Frankfurt, who would have gone top for the first time in 25 years with a victory, are one point back in third.
Leipzig extended their unbeaten club record Bundesliga run to 17 matches from Lois Openda's 59th minute winner in Heidenheim.
It was the fifth clean sheet from the six games for Leipzig who have not conceded in 405 league minutes.
"In the end it is a dirty 1-0 away from home, we happily take it," Leipzig defender David Raum said.
