In a game of very few chances, the first-half substitute fired home the only goal 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 Casper Ankergren from eight yards out.
Jermaine Beckford, the West Yorkshire club's leading scorer, forced a strong save from Lions keeper David Forde just two minutes in as the visitors exploded out of the blocks.
His venomous volley looked set for the bottom corner but for a strong left hand from Forde.
An early Millwall chance fell to full-back Andy Frampton but he volleyed well wide on eight minutes after the ball fell neatly in the penalty box.
The Lions bossed the midfield exchanges as the visitors seemed satisfied with a goalless draw.
Harris, on for the injured Jason Price, caused trouble down the right on 37 minutes when he cut inside only for Naylor to block his curling left-foot effort.
Luciano Becchio blasted a searing volley inches wide just before the break after a neat lay-off from Beckford.
Teen sensation Fabian Delph was lucky not to see red for his horror challenge on Gary Alexander seconds before the interval.
A sensational intervention by Leeds rock Sam Sodje stopped Zak Whitbread getting on the end of James Henry's in-swinging free-kick but the breakthrough came on 71 minutes after some good work by Alexander down the right channel.
He lashed the ball into the box and Naylor's untimely slip left Harris with the space he needed to bury into the bottom corner and take the tie up to Elland Road with his side in the ascendancy.
Simon Grayson's men failed to get going after the break and it was the hosts who continued to look the most likely to get a second in the dying minutes.