Blackburn beat Chelsea on pens
In a roller-coaster match that saw the Premier League leaders twice fall behind only to grab a dramatic 122nd-minute equaliser, it was left to teenager Gael Kakuta to fluff the decisive penalty kick.
Big-spending Manchester City beat a young Arsenal team 3-0 in the night's other quarter-final to set up a mouth-watering clash with holders and local rivals Manchester United in the last four.
With manager Sam Allardyce absent after undergoing heart surgery, Blackburn went ahead when Croatian striker Nikola Kalinic sidefooted home in the ninth minute.
Chelsea manager Carlo Ancelotti responded with a triple substitution at halftime and the gamble paid dividends three minutes later when striker Didier Drogba headed in with almost his first touch of the ball.
Salomon Kalou, sent clean through with only goalkeeper Paul Robinson to beat, calmly slotted in four minutes later to make it 2-1 to Chelsea but Blackburn levelled when keeper Hilario completely missed an intended cross by Brett Emerton.
Kalou then limped off injured in the 73rd minute, leaving Chelsea with only 10 men.
Blackburn went back in front in extra time with a Benni McCarthy penalty before Robinson flapped at a cross from the left and Paulo Ferreira grabbed Chelsea's third goal in time added on.
Kalinic and Chelsea's Michael Ballack both missed in the shootout before Robinson saved a weak attempt from Kakuta.
"We are disappointed but we have to look at the match, I think that the first half was not good but the second and extra time was very good," Ancelotti told Sky Sports television.
"We played 10 against 11 and showed a very good mental attitude and spirit."
Blackburn's assistant manager Neil McDonald praised his players' spirit: "You always have to have the belief," he said.
"We always felt that if they changed the team we could get at them and try and stop the flow of football."
Manchester City, who have recorded seven successive draws in the Premier League, clinched their first appearance in a domestic cup semi-final since 1981.
After going in 0-0 at the break, they stamped their authority on Arsenal with second-half goals from Carlos Tevez, Shaun Wright-Phillips and Vladimir Weiss.
United beat Tottenham Hotspur 2-0 at Old Trafford on Tuesday while Villa cruised past Portsmouth 4-2 at Fratton Park.