With the 16,013 blue and gold faithful in full voice, blockbusting winger Semi Radradra scored a hat-trick in one of the finest all-round games of his impressive career to date but it was a resurgent Inglis, moved to five-eighth for the first time since 2011 who imposed himself on the second half to drag his side to victory by helping create two tries in the final 10 minutes to steal the win.
Desperately needing a victory for what would be their first legitimate one of the year since getting under the salary cap, Parramatta stumbled at the first hurdle and now need a likely 12 wins from 14 games to launch an unlikely finals charge.
With emotion always likely to be running high, a series of huge hits left the Eels down to one man on the bench for much of the second half with Kenny Edwards the victim of an accidental Inglis forearm in the first half to end his night early and Danny Wicks, David Gower, Beau Scott and Isaac De Gois all going for concussion checks at different stages.
Souths weren't without their concerns, losing winger Michael Oldfield in the first half to a hamstring injury and Jason Clark to a head knock. Paul Carter probably should have been taken for a concussion check after going low on Radradra early.
The first half revealed a much-improved Souths defence, with the line racing up to pressure the Eels and looking the best it has since the first two rounds, led in large part by Carter and Sam Burgess, who each had wonderful all-round games.
They turned away the Eels and threatened to ruin the script early for the home fans when a nice cut-out pass from Alex Johnston put Michael Oldfield over for the first try of the game.
An Adam Reynolds penalty goal made it 6-0 shortly but the Eels dominated proceedings for the rest of the half.
A nice Corey Norman cross-field chip to a leaping Radradra got it back to 6-4 before the flying Fijian earned his double shortly after when a brilliant Manu Ma'u offload sent Michael Jennings screaming into space before finding Radradra in support.
The 10-6 scoreline already felt a little unfair on Souths after how well they had defended but it got worse in the seconds before half-time when Alex Johnston spilled a high bomb in front of his line and from the next set a right-side move saw Vai Toutai smash through three defenders to plant the ball down.
A somewhat fortuitous penalty for the Eels, with a high shot on Nathan Brown ruled against De Gois, put the Eels on the attack right after half-time and the Rabbitohs' new right edge of Kyle Turner at centre and Auva'a on the wing were powerless to stop Radradra gliding over for his hat-trick.
At 20-6 the Eels looked a chance of grinding out a win but with Wicks and Gower spending time in the concussion bin and Edwards ruled out a lack of troops on the bench started to tell and despite a few attacking chances Souths started to claw their way back.
A Wicks lost ball put Souths in range for Auva'a to cash in on an overlap before a clever Carter charge down and even more clever toe-ahead was unlucky not to lead to points when Reynolds was ruled to knock on in the grounding.
A series of huge defensive efforts from Parramatta repelled Souths several times through the middle of the second half but another Wicks error – having done well to run the ball out of his in-goal – led to a nice cut-out from Luke Keary (injected off the bench in the 55th minute) put Bryson Goodwin over. Reynolds hit the posts for the second time from touch to keep it at 20-16.
The undermanned Eels were out on their feet and desperately trying to cling to their narrow lead but a long-range Inglis run down the left edge – his second since moving to centre to facilitate Keary's injection – was followed by a beautiful offload to Goodwin who found Keary in support.
Having hit the woodwork twice from the left touchline, Reynolds took his time and moved the tee back outside 30 metres, had a long look and lined up the match-winning conversion that snapped a four-match losing streak for his team and shift the Eels' finals hopes from unlikely to near-impossible
(Oldfield, Auva'a, Goodwin, Keary tries; Reynolds 2 goals) def (Radradra 3, Toutai tries; Gordon 2 goals) at Pirtek Stadium. Half time: Eels 14-6. Crowd: 16,013.