In his 142nd and final Eels game before moving to Newcastle on a 10-year deal that is the richest in NRL history, Brown scored the opening try as Parra embarrassed the Knights.
Newcastle, in coach Adam O'Brien's last game at the helm, struggled to match the intensity of the Eels, who raced to a 34-4 halftime lead at CommBank Stadium and never looked back.
O'Brien announced late last month he would leave his contract two years ahead of its expiry, but Sunday's performance proved simply changing the coach will not fix the Knights' issues.
Newcastle finished with 58 missed tackles, lacked power up the middle and had no answer to an Eels side that was more than happy to throw the ball around.
After Brown's second minute opener, Mitchell Moses bagged a first-half hat-trick and was followed over the line by Matt Doorey and hooker Ryley Smith.
Newcastle's only first-half try came when Jermaine McEwen dived on a grubber kick to the in-goal.
But things just kept growing worse for Newcastle as halfback Jack Cogger and fullback Fletcher Hunt went off in the first half and did not return after failing head injury assessments.
Halftime was only a pause in the onslaught as the free-flowing Eels continued to run amok against a makeshift Knights side.
Parramatta began the second half with a bang, cruising over for three tries in the first 10 minutes.
Josh Addo-Carr scored two of them, the winger racing onto a well-weighted Moses kick over the defensive line before going over off his own chip and chase.
Prop Junior Paulo touched down soon after Addo-Carr to take the Eels past 50 points.
Winger Greg Marzhew briefly stemmed the bleeding for the Knights with a well-taken try in the left corner but it was a mere consolation as Newcastle finished the season with their first wooden spoon since 2017.
Addo-Carr completed his hat-trick, with Tallyn Da Silva and Will Penisini crashing over in the final 10 minutes to condemn the Knights to the third-biggest defeat in their history.
