Record Millwall goalscorer Neil Harris scored the goal to give his side a vital 1-0 first leg win and full advantage
In a game of very few chances, the first-half substitute fired home the only goal in a fierce encounter 20 minutes from time.
His composed reaction from Richard Naylor's unfortunate slip gave the goal poacher the room he needed to fire past the stranded Leeds keeper Casper Ankergren from eight yards out.
The second leg takes place at Elland Road next Thursday.