Visiting winger Luke Varney saw red just three minutes into the second half for an elbow, albeit not malicious, which struck Adam Smith in the face.
Millwall, who had enjoyed the better of a largely lacklustre first half, subsequently took the game to the visitors and went close on more than one occasion.
But they did not do enough to trouble Paddy Kenny between the posts, with Leeds – who provided little threat of their own all afternoon – deserving some credit for holding their own.
That was until five minutes from time when Shane Lowry’s left-wing cross was met by the head of New Zealand international Wood from close range at the far post, a seventh goal of the season for the West Brom loanee.
It was enough to inflict a third successive defeat on Leeds, who fell to an emphatic 6-1 home reverse against Watford last weekend, and left the Yorkshire outfit winless in seven.
Amid a sloppy opening to proceedings, Millwall’s Liam Feeney was first to trouble the scoreline with a shot from distance which flew over the crossbar.
Liam Trotter fired an effort narrowly wide for the Lions before Mark Beevers saw a header cleared off the line by Tom Lees. Andy Keogh’s near-post effort brought a save out of Kenny, the first of either keeper, in the 41st minute.
Keogh arguably came the closest to breaking the deadlock in the first half just three minutes later as his fine right-footed effort from the left channel flew past Kenny and wide of the target.
But an ordinary first half was soon forgotten within three minutes of the restart as Varney saw red, his flailing arm finding the face of Smith as he backed into the Lions defender.
The red card immediately cranked up the atmosphere in the stands and upped Millwall’s tempo on the pitch.
Wood fired over when he really should have passed with team-mates well placed before Leeds defender Lee Peltier headed off the line.
The home side were turning the screw and Chris Taylor and substitute James Henry fired just wide in quick succession after the hour mark. However, the initial burst of goalmouth action was succeeded by very little until Wood’s 85th-minute winner as Leeds appeared set for a creditable point.