The winger struck his seventh goal this season after a 23rd minute counter-attack began with an unconvincing punch out from Villa keeper Brad Guzan and ended with Milner, unmarked in the area, angling his shot home from a superb Stewart Downing cross.
VIDEO: Watch Milner's first-leg winner
Villa manager Martin O'Neill told Sky Sports the semi-final was still finely balanced despite his team's win.
"In a week's time it's going to be every bit as difficult as tonight," he said.
"The tie is in the balance, it's that close based on what I saw from them in the second half - although we played splendidly tonight and probably deserved to win by a bigger margin."
Blackburn manager Sam Allardyce added: "We gave a spirited performance in the second half and needed it.
"We got caught by a sucker-punch on the break for their goal - that's their strength and we allowed them a soft goal and made life difficult for us. Next time, hopefully, it will turn in our favour."
