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, who have won the League Cup five times, are now favourites to reach the 50th final against holders Manchester United or Manchester City at Wembley Stadium on Feb. 28.
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."
BOOED OFF
Rovers, who beat Chelsea in the last round on penalties but are now without a win over 90 minutes in 12 matches, were largely overwhelmed in the first half and booed off at the break.
However, they improved in the second period and Nikola Kalinic was unlucky not to score after hitting the same post twice, first with a header then with a well-struck low curling shot.
Villa who knocked Rovers out of the FA Cup at Villa Park earlier this month, also nearly added to their tally with Milner, Ashley Young and Gabriel Agbonlahor all going close.
The teams meet again in the second leg at Villa Park next Wednesday.
