Moses showed no signs of rust on his return to club duties after inspiring the Blues to a 38-18 win over Queensland in Melbourne on Wednesday.
The playmaker scored two tries and had a hand in two more at McDonald Jones Stadium on Saturday, but he could not stop the Eels falling to a third consecutive loss.
The Eels are last on the NRL ladder with just one win since mid April.
Newcastle, meanwhile, are knocking on the door for the top eight, denied a finals spot by virtue of their inferior points differential.
Parramatta looked set to buck their ugly run of form when some quick-thinking Moses kicking gave the Eels a 12th-minute lead.
The No.7 forced a goal line drop-out with a third-tackle chipkick and on the ensuing set he took control, sending the ball wide for Blaize Talagi to bag the opener.
A bunker review denied Maika Sivo a chance to double the Eels' tally, the Fijian winger arguing he had scored only for replays unable to clearly show grounding on the line.
The Knights breathed a sigh of relief and went down the other end and crossed through debutant Will Pryce - watched on by his father, English great Leon Pryce - after a Daniel Saifiti offload in heavy traffic.
Moses touched down off a scrum play to restore the Eels' lead before Greg Marzhew barged his way over to have the hosts trailing 12-10 at halftime.
Mitchell Moses celebrates one of his two four-pointers in the Eels' loss to Newcastle. (Gregg Porteous/AAP PHOTOS)
Newcastle winger Marzhew and Talagi both went in early into the second half before the two sides had tries chalked off by the bunker.
Newcastle centre Bradman Best failed to ground the ball and Talagi, who was hunting his hat-trick, was ruled to have knocked on in the process of touching down.
Moses took matters into his own hands, surging down the left in the 60th minute to add his second try.
Enari Tuala hit back for Newcastle before Best profited from a Talagi handling error on the Knights' 10m line to race in and give the home side an eight-point buffer.
Junior Paulo crashed over next to the posts to cut Newcastle's advantage to two with five minutes left.
But as the Eels hunted for a winner, Best picked up another loose ball and streaked away for his second try to seal a Knights victory.