Up 14-6 at the break courtesy of a Kenny Edwards' try - set up by Foran - on the stroke of halftime, the Cowboys' Justin O'Neill reduced the deficit to four off a Johnathan Thurston pass early in the second half.
But that was one of the rare times the Cowboys entered the Eels' zone, with numerous attacking raids brought undone by a decisive and energetic Parramatta defence.
At one stage in the second half, Parramatta prop Junior Paulo rocked Thurston with a hit that shook Pirtek Stadium and lifted his teammates to another gear.
A crashing try to Brad Takairangi in the 62nd minute - also assisted by Foran - kicked their lead out to 10 before Taumalolo crashed over in the final minute to set up a grandstand finish.
But the Eels' defence held on, scoring what could be a season-defining win.
Parramatta's Manu Ma'u was put on report for a high shot on Cowboys winger Kyle Feldt in the 48th minute, while Matt Scott could also be in trouble for a crusher tackle on Edwards in the 54th.
-AAP