Moses now appears the most likely contender to replace Nathan Cleary in the NSW No. 7 jumper for Game II in Brisbane on June 21 when Brad Fittler names his squad on Tuesday.
The Lebanon international, whose sole Blues appearance came in 2021 when he played for 70 minutes with a back fracture, set up two tries as the Eels ran up a third straight win for the first time this season.
The halfback was the star attraction in front of a 33,866 strong crowd at Accor Stadium on Monday.
Moses not only strengthened his selection claim, he all but put an end to those of Canterbury prop Tevita Pangai Jr.
Pangai made his debut for the Blues in Game I and had been considered an outside chance to return.
But Moses put paid to that, twice coaxing the Bulldogs prop out of the defensive line with Eels captain Clint Gutherson strolling through the gap he had vacated to score.
Gutherson registered a first-half hat-trick for the Eels with Bailey Simonsson scoring Parramatta's other try as they raced out to a 24-6 lead at the interval.
Simsonsson profited from a busting run from Eels five-eighth Daejarn Asi, who replaced stood-down playmaker Dylan Brown.
Brown awaits a court date to contest allegations that he sexually touched a woman without consent.
Matt Burton grabbed Canterbury's sole first-half try after some neat inter-play with rookie halfback Karl Oloapu.
But bar a few trademark torpedo kicks and a skirmish on the stroke of halftime with Moses, Burton was kept relatively quiet by the Eels defence.
Will Penisini scored for the Eels soon after the halftime break and it looked as if the Bulldogs would wilt with the scores stacked against them.
The introduction of playmaker Khaled Rajab proved the spark for the Bulldogs, the lively 21-year-old had his hands all over a set that finished with Hayze Perham touching down with 20 minutes to go.
Any hope of a comeback was quickly killed off when Parramatta's Fijian winger Maika Sivo bagged a late try, surpassing fellow countryman Semi Radradra to become the fifth-best Eels tryscorer of all-time with 83 in 97 NRL games.