Nick Barmby ensured Leeds breathed a sigh of relief on a night of frustration in the Ukraine as he scored the goal that took Terry Venables' side through to round two of the Uefa Cup.
Barmby struck with 14 minutes left after Alan Smith's header had dropped to him at the far post in front of a gaping goal.
Zaporizhia, 12th of 16 teams in the Ukrainian Premier League and with just eight goals in their 11 matches, made life tough for Venables' team.
They snapped and snarled every time a Leeds player had the ball, but the tackles that rained in from the home side were all too often woefully late.
So much so that Venables complained to the fourth official, with the United manager also voicing concerns about the state of the pitch.
Leeds' defenders were ordered not to attempt any backpasses during the game as the pitch cut up badly.
But the home side simply cut up rough and Bakke should have won a penalty when he was clearly wrestled at a free-kick.
But Venables could have had few complains about the Zaporizhzhya goal on 24 minutes as the home side suddenly burst to life.
Brazilian winger Fabio Vasconcelos cut inside from the right and left the Leeds defence standing as he smashed a left-foot shot against the visitors' crossbar.
Goalkeeper Paul Robinson was still scrambling back when Modebadze connected with the rebound and his looping header beat the stranded Robinson who was left groping at thin air.
The goal squared the tie after Leeds' 1-0 first-leg win but Venables' side had chances to claim the all-important away goal.
Bakke headed over from close range and Smith so nearly caught out goalkeeper Glushchenko with a cheeky chip after Leeds' best move of the first half.
And the erratic keeper somehow held on to a stinging shot from Dominic Matteo after the home side had failed to clear a corner.
Bowyer wasted Leeds' best chance seven minutes into the second half when he sliced wide at the back post after Ian Harte's free-kick had flown across the face of goal.
But the visitors finally made the breakthough on 76 minutes when Kewell's good work down the left found Smith, whose misguided header fell perfectly for the grateful Barmby.
The home side vented their frustration in the shape of one last dreadful tackle from Uros Milosavijevic, whose resulting red card saw him have the final word on an ugly night.
Metalurg Zaporizhzhya: Glushchenko, Valuta, Dodic, Raty,
Visevic, Vasconcelos, Klyuchyk, Milosavijevic, Akopyan, Lapko,
Modebadze.
Subs not used: Zolna, Savinov, Baston, Toledo, Blanchim Hansen,
Ivashchenko, Zayats.
Sent off: Milosavijevic
Booked: Milosavijevic, Modebadze.
Leeds: Robinson, Kelly, Mills, Matteo (Duberry 90), Harte,
Bakke, McPhail, Barmby, Bowyer, Smith, Kewell.
Subs not used: Martyn, Viduka, Okon, Burns, McMaster, Dacourt
Referee: M Bosat (Turkey).