Carling Cup holders Chelsea needed two late goals to reach the last eight as Frank Lampard grabbed a hat-trick.
Gareth McAuley's header gave Leicester an early lead, but the home side went in at the break in front, thanks to two calm finishes from captain Lampard.
Keeper Marton Fulop kept Leicester in the game and DJ Campbell's header set up a tense finale at Stamford Bridge.
Carl Cort's tap-in put the Foxes ahead, but Shevchenko with a rasping shot and a Lampard header turned the tie.
606: DEBATE
Leicester gave an early taste that they had not arrived as sacrificial lambs when their captain McAuley rose unchallenged to head home a free-kick.
Before Wednesday Lampard had not scored since August, but the England midfielder got back in the goalscoring groove when he finished off a three-man move to equalise.
Scott Sinclair played a key role in that goal and the youngster set up Chelsea's second when his cross bobbled loose to Lampard, who volleyed home.
Fulop made three crucial saves, twice denying Claudio Pizarro and pushing an effort from Sinclair on to the post.
But the home side lost Paulo Ferreira just after half-time. The right-back was stretchered off with an injury to his right ankle.
Campbell punished Chelsea's profligacy in the 69th minute when he headed Levi Porter's chip over the advancing Cudicini and into the net.
Five minutes later Alan Sheehan's free-kick was missed by everyone except Cort at the far post and the former Wimbledon striker swept the ball home.
But Shevchenko levelled for Chelsea in the 87th minute and in the dying seconds Lampard's header squeezed over the line to provide a dramatic winner.
"We enjoyed the winning and scoring four goals but we didn't like what happened in the game because we conceded three goals.
"More importantly it showed that we have good character. I've never in my life given up until the last moment even if we're losing 2-0.
"In the last 10 minutes the players showed they have a big heart."
"Where we matched them and maybe shaded them was our heart and fighting spirit.
"Chelsea have not been beaten here for 60-odd games. Bigger and better clubs than Leicester have gone away from here with their tails between their legs.
"To have come so close is a bitter pill to swallow but we have to do that."
Chelsea: Cudicini, Belletti, Alex, Ben-Haim (Essien 80), Ferreira (Malouda 52), Wright-Phillips, Sidwell, Lampard, Sinclair (Kalou 78), Shevchenko, Pizarro.
Subs Not Used: Hilario, Obi.
Booked: Sidwell, Ben-Haim.
Goals: Lampard 20, 29, Shevchenko 87, Lampard 90.
Leicester: Fulop, Stearman, McAuley, N'Gotty, Kisnorbo, Sheehan, Newton (Porter 60), Chambers, Kenton, Cort, Fryatt (Campbell 62), Porter (Maybury 80).
Subs Not Used: Henderson, Hellings.
Booked: Newton, Sheehan.
Goals: McAuley 6, Campbell 69, Cort 74.
Att: 40,037.
Ref: Phil Dowd (Staffordshire).
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