Australian international Harry Kewell ensured new Leeds manager David O'Leary avoided the embarrassment of falling flat on his face from a League Cup banana skin.
O'Leary feared coming a cropper at the hands of West Yorkshire rivals Bradford in the first derby between the two sides since United were promoted to the top flight eight years ago.
And the fear was well founded. Early on the pace of former Arsenal player Isiah Rankin and Gareth Whalley caused untold problems as Leeds' back-line was stretched to breaking point, not a sight which would have pleased former Arsenal and Republic of Ireland centre-back legend O'Leary.
The first clear chance came in the 13th minute when City skipper Stuart McCall's through-ball allowed Rankin to turn teenage defender Jonathan Woodgate inside the area.
A first-time left-foot shot from Rankin forced 'keeper Paul Robinson into a save with his legs.
There was further trouble for United's rearguard three minutes later when a Whalley corner was flicked on by Lee Mills for John Dreyer to power a 12-yard header goal-wards, only for Gunnar Halle to clear off the line.
With Leeds back-pedalling, the winner came against the run of play when Kewell suddenly let fly with a speculative 25-yard effort which spun off Whalley and left goalkeeper Gary Walsh rooted. Having gained the lead in the face of considerable pressure Leeds emerged after the break with only one thing in mind - stemming the tide. Bradford barely saw the whites of Robinson's eyes during the second 45 minutes and Leeds effected a comfortable passage into round four in which they'll meet Leicester at Filbert Street.
Leeds: Robinson, Halle, Radebe, Molenaar, Woodgate, Granville, Hopkin, Bowyer, McPhail, Hasselbaink, Kewell. Subs Not Used: Haaland, Wetherall, Wijnhard, Harte, Santos. Booked: Bowyer. Goals: Kewell 28.
Bradford: Walsh, Todd, Dreyer (Lawrence 83), Moore, Jacobs, Blake, McCall, Whalley, Beagrie, Mills, Rankin (Watson 75). Subs Not Used: O'Brien, Pepper, Prudhoe. Booked: Beagrie, Dreyer.
Referee: U Rennie (Sheffield).
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