This was the first meeting between the two sides since they played in the Championship nine years ago, when the Foxes finished top of the table with a tally of 102 points.
They shocked the footballing world by winning the Premier League just two seasons later, as well as winning the FA Cup only two years ago, but Leicester are a significant distance away from those heady heights.
Exiting this competition means they can now concentrate on matters in the league, with the Foxes four places and three points above the drop zone and pondering the unthinkable of relegation.
The hosts actually started brightly, but early missed opportunities proved fatal. Rovers keeper Aynsley Pears denied Tete’s strike and Dennis Praet’s follow-up, before he then kept out Jamie Vardy’s shot from the angle.
But once Blackburn went ahead courtesy of Dolan’s strike from outside the area in the 33rd minute, they showcased a display full of energy and verve.
They deservedly added a second when the sprightly Szmodics got the bounce of the ball and barged his way past the Leicester backline before coolly rolling in his finish.
Jon Dahl Tomasson’s men should have been out of sight, but Leicester’s stand-in keeper Iversen spread himself to keep out a low drive from Szmodics, who twice curled wide.
Iheanacho’s 67th-minute goal produced a nervy finish and the home side almost took the game to extra time.
Nampalys Mendy fired inches wide, while Daniel Amartey’s late header hit the outside of the post.
Blackburn held out for the six minutes of stoppage time, leaving their supporters singing they are “going to Wembley” after a first win at Leicester since 1991 – a run of 10 games.
As well as keeping their Wembley dream alive, Rovers will look to maintain their form in the Championship, as they stretched their excellent recent run to one defeat in their last 13 under Tomasson.
Tielemans out for up to six weeks
In another blow for the Foxes, Rodgers confirmed midfielder Youri Tielemans will be sidelined for up to six weeks with an ankle injury.
The 25-year-old was hurt after coming on as a substitute during Saturday’s defeat by Arsenal.
“Youri will be out for six weeks – six weeks will feel like six months when you lose a player of that quality,” Rodgers said after the Blackburn loss.
“Sadly he’s done the ligaments in his ankle. He won’t be back before the international break.”
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