After a superbly marshalled performance by the visiting side's five-man defence, the Leeds-born Goodman stunned the home crowd with a goal in the 83rd-minute before Segers, called in for only his second senior appearance for the Black Country club, denied Leeds a 89th-minute equaliser by saving a penalty from Jimmy Floyd Hasselbaink.
Segers, the 36-year-old former Wimbledon goalkeeper who stood trial last year alongside John Fashanu and Bruce Grobbelaar, played only after the regular choice Mike Stowell failed to recover from a stomach virus.
After two vital saves from open play had thwarted Leeds on the rare occasions they found a way past Dean Richards, Keith Curle and company, Segers threw himself to his left to palm away Hasselbaink's spot- kick after substitute Robbie Keane's foul on the Dutch striker had offered Leeds salvation following Goodman's strike.
Graham hailed "an excellent performance" by Mark McGhee's side. "They set out their stall and we were never really able to make them sweat," he said. "A draw might have been a fair result but we did not deserve to win."
If the tie was important to Leeds as a means of prolonging their interest in silverware this season, then it was almost as vital to McGhee in his attempt to fulfil his brief at Molineux. Last week, the voluble Wolves manager was booed by the Black Country side's suffering supporters after a squandered home point against Stoke left his side's promotion challenge looking increasingly forlorn.
But he outwitted Leeds yesterday by dropping the 4-4-2 system Graham had anticipated in favour of three centre- backs and recalled both Goodman and Steve Bull against expectations.
The Premiership side thus had more to think about than they had bargained for as McGhee pinned his strategy on a counter-attacking game, smothering Leeds with blanket defence but always retaining the threat of the breakaway.
In the event, save for a couple of early opportunities wasted, Wolves relied on their survival instincts almost until the death as Leeds dictated the play but failed to create openings proportionate to their dominance of possession.
"In truth we did not make that many chances," Graham rued. When Leeds did break through, Segers did his job superbly, saving from Australian teenager Harry Kewell in the first half and rushing from his line to claim the ball at Rod Wallace's feet in the second.
Leeds pounded away and were twice close to nosing ahead when Robert Molenaar evaded his marker to meet Kelly's free- kick with an eight-yard header and when, with 10 minutes remaining, Adrian Williams hacked the ball to safety when Alf Inge Haland seemed to have done enough to end the home crowd's torment.
Then came the moment when the First Division side booked their passage to the semi-finals for the first time since 1981, as Goodman spun into space behind a square Leeds rearguard. Carl Robinson spotted his run and Goodman ended his home-town club's hopes with a chip over Nigel Martyn.
A lifeline offered itself when Keane, an 18-year-old Wolves substitute, rashly brought down Hasselbaink only for the Dutch striker, who missed a last-minute penalty against Leicester in the Premiership last month, to fail again, giving his compatriot a relatively comfortable save.Reuse content