Mark Beevers struck inside the opening 10 minutes to set Millwall on the way to their first opening-day win since 2010.
Beevers got them off to a flyer after a neat short corner routine and Shaun Williams made sure of the result from the penalty spot two minutes from time.
Leeds boss Dave Hockaday said: “From last season we wanted to change the philosophy at the club and get the players comfortable on the ball.
“Having said that, if you get a number of passes and then they start to press then that’s when you get through them, over them, around them but you get behind them with quality. We didn’t do that. We kept passing for passing’s sake, inviting more and more pressure.
“First half we didn’t perform, didn’t stick to the game plan. Having said that, we conceded a poor goal from a corner.
“The good thing is we responded well in the second half. But football’s about moments and we didn’t handle the moments as well as they did.
“We learnt a lot about our players and how they can handle the big occasion. We wanted to stop them carrying out their game plan, which is lots of diagonals, and we allowed them too much time to do it.”