The Millers centre-back stabbed in a close-range shot 13 minutes from the end as Rotherham won for the first time this season at the 21st attempt.
The home side survived a first half that should have seen Leeds several goals ahead and then hit them with a shock winner.
Leeds made a blistering start and could have had a hatful of goals inside the first seven minutes.
In a breathtaking spell Rotherham keeper Mike Pollitt made three super saves and Leeds hit the woodwork three times.
Such was Leeds' dominance in the first half that they notched up eight corners as Rotherham failed to claim one.
With the game only seconds old David Healy had the visiting fans on their feet with a stunning 30-yard strike that Pollitt matched turning it over with a strong one-handed save.
Then Clarke Carlisle smashed in a close-range shot that bounced over Pollitt and hit the crossbar. As the home side struggled to find a way out of their own area Carlisle went close again when he smashed a towering header against the bar.
The big Leeds man then got in another header but this time hit the upright and injured himself in the process. He lasted only four more minutes before hobbling off and being replaced by Frazer Richardson - a former Rotherham schoolboy.
Pollitt was again forced into heroics and dived at the feet of Healy as the Leeds dangerman cut into the area. The visitors went close again when Simon Walton tried a 20-yard effort that Pollitt smothered.
Rotherham's rare moments of relief came when Brazilian striker Junior and Martin Butler broke in behind the Leeds defence.
Michael Proctor had a glorious chance with the second half only a minute old but volleyed high and wide.
But Rotherham had to wait until the 66th minute for their first effort on target when Junior hit a 25-yard curling free-kick that was well held by Neil Sullivan and Rotherham's only corner came 15 minutes from the end.
The home side's second shot on target came two minutes later and gave them the shock lead.
Paul McLaren's free-kick was headed down by Chris Swailes, Shaun Barker back-heeled it on and McIntosh stabbed the ball in from close range.