But the Eels' halves headaches could continue after their other first-choice playmaker Dylan Brown went on report for a high tackle on Saturday night.
Victory at CommBank Stadium temporarily stops the drums beating for coach Brad Arthur, who was vindicated in his decision to roll the dice on a new halves combination.
Dylan Brown was impressive for the Eels but faces an anxious wait after being placed on report. (James Gourley/AAP PHOTOS)
After a quiet first half from both men, Brown and new five-eighth Daejarn Asi combined after the break to put the Eels on their way to a much-needed victory.
Brown put the grubber kick in that helped Morgan Harper to Parramatta's third try shortly after halftime, and looked more comfortable managing the attack than in the two losses since Moses injured his foot.
With 17 minutes to play, Asi skipped through a gaping hole in the Cowboys' defence to make it a 12-point game, and then iced a field goal to confirm the result in the final four minutes.
"DJ (Asi) did a really good job. I was happy for him that he got to ice the moment at the end of the game, so that's pleasing for him," Arthur said.
"We were pretty courageous today.
"It's hard to be at our best every week but the effort was there and there was a real desire."
The Cowboys will rue letting the Eels back into the contest after dominating their hosts early.
They had two tries denied in the first half and looked primed to tear the Eels' makeshift left edge to pieces, with Bailey Simonsson in for Maika Sivo on the wing and Brown attacking on the right.
But the Eels hung in and were clinical enough to hurt the Cowboys, having blown chances with reckless abandon during last week's loss to Canberra.
Joe Ofahengaue crosses for Parramatta's opening try against the Cowboys. (James Gourley/AAP PHOTOS)
The Cowboys produced moments of their trademark dazzling attack, shifting the ball almost acrobatically ahead of a Scott Drinkwater try that cut the deficit to six in the last 10 minutes.
But Asi's first career field goal put paid to any thoughts of a late comeback for a Cowboys side that was too sloppy in the second half.
"When you're chasing the game like that, you need things to go right across the park and Drinky spilt one, Jakey Granville spilt one," Cowboys coach Todd Payten said.
"Some (errors) are skill, some are concentration, some are fatigue, some are communication."
Brown faces a nervous wait after hitting Tom Dearden high in the first half, with Bryce Cartwright also going on report for slamming into the Cowboys' five-eighth after he hit the ground.
The Eels halfback has a clean judiciary record so will escape without suspension if handed a grade-one careless high tackle charge - but anything higher and he will receive a ban.
That would force Parramatta to make more changes to their spine, with a halves combination of Asi and Blaize Talagi appearing the likeliest choice.
"I'd need to watch them again but I didn't think there was much in (Brown and Cartwright's hits) at the time," Arthur said
"(But) I didn't have my glasses on, so I couldn't see real good."
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