After a goalless draw at the King Power Stadium, there were 10 successful kicks before Danny Ward saved Manolo Gabbiadini's attempt. Nampalys Mendy then scored to put Leicester through to the last eight, where they will host Manchester City on 18 December.
It was harsh on Southampton, who had the better chances to win the tie during 90 minutes. But Leicester progressed in the tie rearranged in the wake of the helicopter crash which killed chairman Vichai Srivaddhanaprabha.
Danny Simpson and Fousseni Diabate were handed their first starts of the season as two of nine changes made by Leicester boss Claude Puel. Just Jonny Evans and Demarai Gray retained their places in the starting line-up from Saturday's Premier League draw at Brighton.
Southampton manager Mark Hughes made five changes from the team that lost at Fulham at the weekend as Angus Gunn, Yan Valery, Jack Stephens, Jannick Vestergaard and Michael Obafemi replaced Alex McCarthy, Cedric Soares, Wesley Hoedt, Gabbiadini and Charlie Austin.
It was clear from the outset that Valery, who along with Obafemi was making his full debut for Saints, was in for a busy evening as Gray looked lively down the left and Leicester began on the front foot, putting Southampton under early pressure with a couple of corners.
Saints survived and grew into the tie and created a good opening midway through the first half when Ward had to be quickly off his line to block Obafemi's effort with his feet.
Southampton slowly assumed control, making Leicester defend for long periods, although without troubling Ward.
Jamie Vardy, captain for the night with Wes Morgan only on the bench, endured a frustrating first half but almost caught a lucky break in injury time. He got in behind the defence and his cut-back from the byline was nearly steered into his own net by Vestergaard, but to his relief the ball drifted wide of the post.
Nathan Redmond turned Caglar Soyuncu and Simpson inside out on a mazy run into the penalty area and his shot struck the underside of the crossbar. Obafemi was unable to turn in the rebound on the half-volley from close range.
Shortly afterwards, Pierre-Emile Hojbjerg's effort from the edge of the box brought a decent save from Ward.
Leicester's best moment came with 10 minutes remaining. Gray ran beyond Steven Davis and Soares before flashing a shot narrowly wide from 20 yards which had Gunn worried.
Southampton thought they had broken the deadlock when a weaving run from Redmond was finished off by Davis, but the goal was ruled out by VAR after Redmond was adjudged to have handled the ball.
There was still time for another VAR review at the other end when Evans went down under a challenge but no penalty was awarded.
A superb fingertip save from Ward to divert Gabbiadini's late free-kick on to the crossbar ensured the tie went to penalties, when Ward was the hero again - denying Gabbiadini once more.
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