Adding more pain to the Cowboys and Queensland, halfback Tom Dearden injured his ankle in a tackle and will undergo scans on Saturday, just weeks before State of Origin kicks off on May 27.
On a night when Jason Taumalolo became the most-capped Cowboy (295 games), the Eels upstaged the NRL premiership winners' milestone at Queensland Country Bank Stadium on Friday.
Leading by eight points with less than 10 minutes remaining, the Cowboys were in the box seat to earn their seventh victory in eight games.
But Parramatta flicked a switch as Jordan Samrani crossed in the 75th minute, before Moses orchestrated a try for Joash Papalii to level the scores.
Moses missed the conversion attempt and then a field goal to seal victory.
But with the game going into golden point, the halfback kept his cool to slot the winning field goal, while a penalty for pressuring the kicker was handed to Scott Drinkwater, and the Eels secured another two points.
"I probably should have finished it in time. I felt pretty confident kicking that one from the sideline," Moses said.
"But just the effort that our young boys showed, just the fight to stay in it and come up with some big plays at the end of the game ... was really good to see."
Victory came as Parramatta's player shortage escalated with hooker Ryley Smith (sternum), centre Will Penisini (osteitis pubis), and Jonah Pezet (suspension) all out after the last round.
But North Queensland coughed up a mammoth 17 errors to keep the door ajar for the Eels, and the visitors surged to claim their second win in seven games.
Not only will the Cowboys have to wait on Dearden, but Soni Luke also left the field early with a knee injury after it buckled under a tackle from prop Junior Paulo.
Regardless, Dearden was inspirational, assisting three tries, while hooker Reed Mahoney made a game-high 47 tackles.
"We showed a lack of respect to our most capped player. We showed a lack of respect to our captain with eight minutes to go who was trying to push passes when he's on one leg," coach Todd Payten said.
"I'm angry right at the minute ... We found several ways to lose."
Both teams went tit for tat in the first half as Brian Kelly and Tallyn Da Silva crossed for Parramatta, while second-rower Heilum Luki and the newly re-signed Jake Clifford scored for the Cowboys.
Trailing 12-10 at halftime, Josh Addo-Carr reinstalled the Eels advantage before some silky skills from Jaxon Purdue, and Mahoney helped North Queensland take the lead.
Addo-Carr crossed for his second when he picked off a Dearden pass, but Tom Chester (228 metres) secured a much-deserved four-pointer to inch the Cowboys ahead in the 68th minute.
Samrani stormed over before the centre assisted Papalii to level scores in the 77th minute.
Clifford thought he had notched the game-winning field goal, but it was touched before Moses' attempt was charged down, sending the match into golden point.
The Parramatta halfback stayed composed to guide home the match-clinching field goal.
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