Souths' manic victory came at a cost as young halfback Ashton Ward tore his right hamstring attempting a sideline conversion on Saturday night.
Alex Johnston crossed for three tries as Souths took an imperious 28-0 halftime lead in the veteran winger's first game at Allianz Stadium since breaking the NRL's tryscoring record.
The Eels lost Brian Kelly to the sin bin for a professional foul after just 92 seconds and conceded three tries without him, then watched gun fullback Isaiah Iongi go down with a knee injury just before the break.
Coach Jason Ryles was "very confident" Iongi had not suffered a long-term anterior cruciate ligament injury, but the issue may still be season-ending.
Against all odds, and with no realistic finals hopes to play for, Parramatta were hoisted back into the contest by off-contract journeyman Ronald Volkman.
With Josh Addo-Carr deputising at fullback and hooker Ryley Smith in the centres, five-eighth Volkman's attacking nous threatened to help the Eels pass the standing record for biggest NRL comeback (26 points).
After Tallyn Da Silva crossed for Parramatta's first try, Volkman kicked through for Smith to nab their second before spinning past Matt Dufty for a four-pointer of his own.
When Jordan Samrani soared over makeshift winger Jye Gray and slammed Volkman's kick down, the Eels were within four points.
After forcing a dropout in the final minutes, Parramatta looked set to go for the killer blow, but the returning Tallis Duncan regathered the Rabbitohs' short restart.
In the same set, veteran Cody Walker kicked a 40/20 to put Souths out of trouble and on the attack for the final exchanges of a calamitous game.
The 13th-placed Eels were left to wonder what might have been if not for their sluggish start.
"The second half was what we planned to do and how we planned to play," Ryles said.
"The boys showed an enormous amount of fight and we were unlucky in the end."
Walker had been integral to the Rabbitohs' early lead in Indigenous Round, most memorably slamming a kick into the goalposts that Tevita Tatola regathered for a fantastic try.
The scrappy win lifts Souths back into sixth place on a weekend when top-eight rivals Manly and Canterbury suffered potentially costly defeats.
"I'll take the two points, then after that we'll move on," said South Sydney coach Wayne Bennett.
"That's what we came here for. I'm not going to worry about all the other odds and ends of it."
Newly re-signed halfback Ward needed the assistance of two trainers to leave the field after tearing his hamstring during the first half.
Jayden Sullivan is likely to replace Ward for the big clash against the ninth-placed Bulldogs next week, but Bennett was hopeful he could return this year.
Souths will likely make finals if they win two of their remaining four games, but also have tough matches against the Warriors and Sydney Roosters.
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