Almost exactly a year on from meeting at the same stage of last season's competition, the two sides were once again forced to go the distance after Marc Albrighton had cancelled out Kevin De Bruyne's opener.
Holders Man City now progress through to the semi-finals of the competition as they bid to retain a trophy for the first time in their history, and they will be joined in the last four by League One side Burton Albion after they shocked Middlesbrough this evening.
Both managers rang the changes as Leicester were without the injured Jamie Vardy, while Man City handed a debut to 17-year-old Eric Garcia, although the visitors were also able to start fit-again duo Sergio Aguero and De Bruyne.
The latter was making just his third start of the season due to a succession of injury problems, but it did not take him long to provide a reminder of his quality with the opening goal after only 14 minutes.
De Bruyne skipped away from Hamza Choudhury before whipping his disguised finish into the bottom near corner from 25 yards, with the crispness of his strike preventing Danny Ward from getting across in time.
It could have been two just four minutes later when Brahim Diaz's shot deflected into the path of Riyad Mahrez, but the former Leicester man blazed over from close range on his first return to the King Power Stadium since his £60m summer move.
The hosts responded quite well to going behind, though, and they almost produced an equaliser in the 21st minute when a deflected long-range strike from Demarai Gray needed to be turned past the post by Arijanet Muric.
That was as good as it got for Leicester in the opening 45 minutes, with a wayward Kelechi Iheanacho strike their only other effort, but Man City were struggling to create clear chances of their own as well, despite dominating possession.
Indeed, the holders needed to wait until the second half for their next opportunity, which arrived just two minutes after the restart when Mahrez released Aguero clean through on goal, only for Ward to come out on top in their one-on-one duel.
Aguero was denied by Ward again shortly before the hour mark, but as with the first half Leicester grew into proceedings and Harry Maguire fired a reminder that the hosts were still in the game with a headed chance that went begging.
Mahrez looked particularly intent on getting on the scoresheet against his former club and came within a whisker of doing so moments later with a wicked curling effort from the edge of the area which flashed narrowly over the crossbar.
Leicester were rewarded for staying in the game when they levelled things up with less than 20 minutes remaining as Albrighton latched on to Wilfred Ndidi's pass over the defence before taking the ball down and lashing his half-volley past a helpless Muric.
Mahrez came close again shortly after the equaliser with a low pass across the face of goal which dribbled wide of the far post, and Leicester also survived a penalty shout when Choudhury brought down Gabriel Jesus.
Penalties were eventually required to separate the two sides, though, and Man City appeared to have the early advantage when Fuchs blazed his spot kick over the crossbar.
Raheem Sterling offered a let-off with an attempted Panenka which also sailed over the bar, but Leicester then saw Maddison and Soyuncu both denied by Muric after stuttering run-ups.
Zinchenko made no such mistake by picking out the top corner with his decisive penalty as Man City sealed their place in the last four.
LEICESTER (4-5-1): Ward; Simpson, Soyuncu, Maguire, Fuchs; Ghezzal (Maddison 53'), Choudhury, Iborra (Albrighton 61'), Ndidi, Gray; Iheanacho (Pereira 81')
MAN CITY (4-3-3): Muric; Walker, Garcia, Otamendi, Zinchenko; De Bruyne (Gundogan 71'), Stones, Foden; Mahrez, Aguero (Jesus 76'), Diaz (Sterling 66')