On an Easter Monday of high drama, Parramatta lost another player to a suspected season-ending injury from foul play before Madden stood up when it counted in front of a record crowd at CommBank Stadium.
With both sides trading penalty goals in the final five minutes to take the game to extra time, Madden slotted a shot from 15 metres out in just his second NRL game since July 2024.
The chance came after Eels lock Dylan Walker was called offside as he tried to charge down a Madden field-goal shot, which went just to the right of the posts.
The round-five win sends the Tigers into the top two to finish the weekend for just the second time in the past 12 seasons, the other time coming after round one in 2017.
"Who cares?" Tigers coach Benji Marshall said.
"I hate talking about the past, I think I've made that pretty clear. I've been asked every week about it.
"And it's the same answer - we're a different team. It's completely different. It's different people, different staff and different players."
Earlier, train-and-trial player Apa Twidle came on for his NRL debut as 18th man and inspired Parramatta back into the contest from 18-10 down just after half time.
Twidle had appeared unlikely to take the field on Easter Monday before 29,397 fans - CommBank Stadium's record crowd.
The 21-year-old was granted an exemption to be included in the game-day team following an Eels injury crisis that deepened when Bailey Simonsson (dislocated ankle), Sean Russell (head knock) and Jonah Pezet (hamstring) went down against the Tigers.
Twidle also received treatment for a minor shoulder injury after the game but is expected to be named in the side to face Gold Coast on Sunday.
Eels coach Jason Ryles smiled when asked about his side's attitude in the face of adversity on Easter Monday.
"Adversity. It was adversity, all right," he said.
"It was obviously not the result we were looking for but I just said to the players then, the performance is what really matters tonight.
"If we continue to show that each week, we're going to win more games than we lose."
Simonsson left the field in a medicab after landing awkwardly from a mid-air tackle by Luke Laulilii, sin-binned soon after giving the Tigers an 18-10 lead with his second-half aerial try.
Laulilii can accept a one-game suspension after being charged with grade-two dangerous contact.
The Eels fear Simonsson, who was rushed to hospital, will be sidelined for the remainder of the season.
Twidle scored with the first touch of his NRL debut with a stunning put-down on the right edge that was initially ruled a no try.
Twidle's second was at least slightly simpler than his first, running onto a Mitch Moses cut-out ball and getting outside Hemasi Makasini to sprint to the line.
His efforts allowed the Eels to draw level at 18-18.
In the final five minutes, Mitch Moses tore down the right side on the fifth tackle and was stopped by Samuela Fainu.
Referee Peter Gough initially ruled the set complete, but when the Eels launched a captain's challenge, the bunker picked up a high tackle that allowed Moses to kick for a two-point lead.
But the Tigers equalised on the following set when Sam Tuivaiti hit Sione Fainu high, with Madden tying the game at 20 by slotting the first of two crucial penalty goals.
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