That they did so after having their prop forward, Barrie McDermott, sent off inside the first 20 minutes yesterday, only underlined the scale of their achievement.
They have had days at Headingley before when they thought they had caught up with Wigan, but the way they took their revenge for last year's Super League Grand Final defeat yesterday suggested that they might finally be right.
McDermott, the former Wigan front-rower whose career has been littered with these excesses, went off for a horrible high tackle on Simon Haughton, after playing particularly well in the first quarter. Before his self- control snapped, he had contributed to a tremendous, 100 miles-per-hour start by Leeds that brought them a try in the 10th minute when Iestyn Harris and Adrian Morley sent Brad Godden through, Harris landing the first of his goals from the touchline.
Andy Farrell had pulled back two points with a penalty, but Wigan had barely got into the game before McDermott's dismissal.
"When that happens you think that Wigan might steamroller you," said Leeds' coach, Graham Murray. "Fortunately our players didn't believe that."
Leeds showed they had no intention of bowing to the inevitable by extending their lead, Harris dropping a goal and Daryl Powell then throwing the long pass that enabled Leroy Rivett to shimmy through and score when Paul Johnson showed him too much of the touchline.
Harris again converted from wide out, but Wigan at last seemed to be asserting their advantage when Farrell and Greg Florimo sent Haughton striding through for a try which Farrell converted.
Immediately before half-time they looked to be taking control when a sweeping cross-field move, again involving Farrell and Florimo ended with Gary Connolly sending in Kris Radlinski.
A one-point lead was surely not enough for Leeds with 40 gruelling minutes still to play, but they scarcely allowed Wigan into the game in the second half.
Their one golden opportunity came after 56 minutes when Jason Robinson came racing out of his own half on the last tackle but Mark Reber, fresh off the plane from Australia and thrown into a high-pressure match, knocked on with three men outside him, any one of whom could have scored.
Within a minute Leeds's man of the match, Ryan Sheridan, had dropped a goal and a Harris penalty nudged his side further ahead.
The game was then won by two tries in four minutes. Marcus St Hilaire burrowed his way over after Andy Hay was stopped on the line with Farrell going to the sin-bin for protesting too graphically and Sheridan capped his personal contribution with another short-range effort after Godden had been halted. Leeds finished with the luxury of a Wigan try four minutes from time not mattering in the slightest.
"It's the proudest I've been of a football team in my life," said Murray, who detected a new depth of self-belief in his side.
"It looked like the same Leeds teams to me," said Wigan's John Monie, who has perhaps not picked the ideal week to discuss an extension to his contract. "It was us who were down on our performance."
Leeds' reward for their epic victory is a home tie almost as difficult in the next round against St Helens.
"It's not the best draw, but that's what we thought when we came out of the hat with Wigan," said the Leeds captain, Iestyn Harris.
"St Helens are a great side, but we will be full of confidence after today."
The tie between Huddersfield and Salford is likely to be the BBC's other televised game on the weekend of 27 to 28 February, with the all Super League clash between Warrington and Halifax the other highlight of the draw.
Leeds: Harris; Rivett, Blackmore, Godden, Cummins; Powell, Sheridan; Fleary, Newton, McDermott, Morley, Anthony Farrell, Glanville. Substitutes used: St Hilaire, Jackson, Hay, Mathiou.
Wigan: Radlinski; Robinson, Moore, Connolly, P Johnson; Florimo, Reber; O'Connor, Cassidy, Mestrov, Gilmore, Haughton, Andy Farrell. Substitutes used: Cowie, Davies, Goldspink, A Johnson.
Referee: R Smith (Castleford).
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