The big centre-half headed a Rory Delap long throw past Shay Given, just as he did in stoppage time eight days earlier in the Premier League, only this time his effort stood.
Manchester City were down to 10 men by the time Shawcross struck in the 95th minute, with Emmanuel Adebayor sent off for swinging a hand into Shawcross' face.
And Stoke sealed their place in the last eight for the first time in 38 years when substitute Sanli Tuncay collected Glenn Whelan's 99th minute pass and danced past two defenders before burying a left-foot finish.
Stoke made an unusually tentative start and Adebayor almost made them pay with a fierce 25-yard drive which forced a flying save from Thomas Sorensen.
And the visitors continued to dominate as Vincent Kompany, a powerful presence in the middle of the field, and Gareth Barry both failed to put away half-chances.
The recalled Craig Bellamy should have put Manchester City ahead in the 20th minute after Adebayor turned Dean Whitehead far too easily on the halfway line.
Adebayor then played in Bellamy, but the Wales international took too long to shoot and Sorensen dashed from goal to save.
Stoke finally started to show signs of warming to the task as a series of corners and Delap long throws ramped up some pressure.
Shawcross had a shot charged down close to goal and Delap's header was clutched under the crossbar by the previously redundant Given.
But a disappointing first half, which certainly didn't live up to expectations, fizzled out with some untidy play from both sides.
Stoke came out for the second half as if they had been given a rocket and the tempo finally began to resemble an FA Cup tie between two top tier teams.
But the visiting defence, with Joleon Lescott marshalling operations, held firm against the increasing menace of Ricardo Fuller and 55th minute substitute Tuncay.
Roberto Mancini introduced Shaun Wright-Phillips in an attempt to pep up his troops and it almost worked in the 67th minute when the winger's cross was headed over by Barry.
But it was another substitute, Stoke's forgotten man Dave Kitson, who broke the deadlock in the 78th minute.
The former Reading forward linked well with Tuncay before placing a low, left-foot shot beyond the stranded Given.
Stoke's lead lasted less than three minutes as Adebayor chested the ball into the path of Bellamy, who threaded his 12-yard shot through the eye of a needle and inside Sorensen's near post.
But Adebayor was given his marching orders a minute later and Stoke took full advantage of their extra man.