Saints, who broke Wigan's eight-year sequence of Cup wins last season but had not beaten them in the competition for 20 years, had been in charge for most of the first half.
But when Goulding's high tackle on Neil Cowie sparked a mass brawl that was finally resolved by the referee, Russell Smith, brandishing the red card, it seemed that Saints were destined to squander a wonderful opportunity.
Wigan, flat and ragged as they were, would surely make their one-man advantage tell in the remaining 40 minutes. Instead, Saints produced the grittiest and most courageous of performances not only to beat them but to dominate them more and more convincingly as the game went on.
"What we spoke about at half-time was belief in ourselves and in our abilities," Shaun McRae, the St Helens coach, said. "We had two options. We could either throw the towel in and give Wigan the ball game or we could fight. We chose to fight and it was the best fighting performance I have ever been associated with."
Saints' determination was immediately obvious in the way they retook the lead that Wigan had whittled away. The Australian forward Derek McVey, who had given a half-time oration of his own to urge his teammates not to use Goulding's sending-off as an excuse, gave his feelings practical expression by sending Karle Hammond away with a superb pass.
Although Tommy Martyn was stopped short of the tryline, Hammond, who along with Apollo Perelini stood out, forced his way over from close range.
The most that Wigan could manage was a penalty from Andy Farrell. As the Wigan captain admitted, they could never get their game flowing and they conceded far too many penalties, often by failing to come to terms with new interpretations of the rules at the play-the-ball.
Whether by coincidence or not, none of Wigan's returnees from winters in rugby union was remotely close to his best and the speculation is now rife that one of them, Va'aiga Tuigamala, will be leaving for Newcastle. If that is the case, his last game for Wigan was not one he will choose to remember.
Saints, on the other hand, will relish this win for a long time. After Martyn, kicking in place of Goulding, had landed a penalty, two tries in the last seven minutes underlined their superiority on the day. The first came when Martyn wriggled his way to within sight of the tryline and Paul Newlove, with whom Farrell waged a feud for most of the half, plunged over.
With Wigan becoming desperate, Henry Paul's speculative pass was picked off by Alan Hunte, who went half the length of the field to round off a famous victory. "They had that look in their eyes all week," McRae said. "They wanted it really badly."
If that determination had been sharpened by Goulding's exit, it was also there for all to see from the very start of the match, when two goals from Goulding and a try from Perelini gave them an eight-point lead.
An exchange of penalties left that gap intact until Paul and Jason Robinson combined to give Kris Radlinski the overlap for Wigan's only try six minutes before half-time.
Saints got the taste of cup glory last year and anyone who hopes to deprive them of it will have to play far better than Wigan did yesterday.
St Helens: Prescott; Arnold, Hunte, Newlove, Sullivan; Martyn, Goulding; Perelini, Cunningham, O'Neill, Joynt, McVey, Hammond. Substitutes used: Matautia, Morley, Pickavance.
Wigan: Radlinski; Ellison, A Johnson, Tuigamala, Robinson; Paul, Edwards; O'Connor, Hall, Cowie, Haughton, Cassidy, Farrell. Substitutes used: Holgate, Long.
Referee: R Smith (Castleford).Reuse content