Moses' return from a foot injury has barely rated a mention over the past week as Galvin's contractual status at the Tigers has dominated headlines.
Galvin was dropped to NSW Cup by the Tigers after raising concerns with the coaching of Benji Marshall and stating he would not sign a new deal.
Without the teenage five-eighth at CommBank Stadium on Monday, the Tigers lacked spark and were incredibly ill-disciplined.
Moses, by contrast, kept his cool - even when the Eels were down to 11 men at one point - and set up Bailey Simonsson with a chip kick to clinch the win.
"He (Moses) just has a presence in our footy team and when he plays, we're a little bit more organised for longer," said Eels coach Jason Ryles, who was shadowed by ex-Wallabies coach Eddie Jones in his box.
"His kicking game certainly helps us, he's a quality player and I'm glad we've got him."
How Marshall could have done with a calming influence like Moses.
After their club was subjected to intense media scrutiny all week, the Tigers faltered under the spotlight.
Winger Sunia Turuva was sin-binned for igniting a second-half brawl.
Veteran utility Jack Bird petulantly threw an opponent's head gear away, missed the ensuing tackle that led to a try, then gave away a penalty on the restart.
He did not return and Marshall said such behaviour was "not good enough".
Earlier on Sunday, Galvin had played in a Western Suburbs side at Lidcombe Oval, and it remains to be seen how much longer he languishes in reserve grade.
Marshall was loathe to discuss Galvin's status amid claim's the five-eighth's camp feel he is being bullied out of the club.
"It's been a big week, no doubt, so to get out there and try and play is the first part," Marshall said.
"But I don't think that was an excuse for some of the things that happened today."
There is every chance that when Galvin does leave the Tigers, he joins Moses at the Eels (2-5) after Ryles spoke of his desire to lure the teen prodigy to Parramatta earlier this week.
Moses got Parramatta off to a hot start, kicking a 40/20 and setting up Josh Addo-Carr for the opening try of the afternoon.
Tries from Terrell May and Jahream Bula got the Tigers ahead, before Eels fullback Isaiah Iongi scored to make it 10-10 at the break.
But things quickly began to unravel for the Tigers, who leaked three tries in six minutes when Samuela Fainu was penalised for a questionable hip-drop tackle on Kelma Tuilagi.
Back-rower Tuilagi, Sam Tuivaiti and Iongi crossed in quick succession as Bird was hooked for a run of brain explosions.
Turuva was the next Tiger to lose his cool and he and Eels forward Luca Moretti were sent to the sin bin for their roles in an all-in melee.
Iongi was sin-binned for a tackle without the ball, reducing the Eels to 11 as they fought to preserve a 16-point lead.
The Tigers cut the deficit with tries to Alex Seyfarth and Luke Laulilii.
But Moses chipped over the top for Simonsson, before Addo-Carr grabbed his second to truly put the game beyond the Tigers' reach.
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