Teenage forward Rolando Aarons put Alan Pardew’s side ahead in the sixth minute and substitute Moussa Sissoko added a superb solo goal 14 minutes from time to send Newcastle into the quarter-finals.
“It’s a marvellous performance from Newcastle tonight. Everything we wanted and tried to get from the game came off,” said Pardew, whose side will visit Tottenham Hotspur in the last eight.
Premier League champions City, who saw midfielder David Silva forced off by injury, have now gone three games without victory in all competitions ahead of Sunday’s derby with Manchester United.
“We didn’t play well enough,” City manager Manuel Pellegrini told Sky Sports. “We conceded two easy goals and didn’t take our chances to score.”
Ryan Taylor was making his first Newcastle appearance since August 2012 after a long-term knee problem and he quickly made an impact.
Taylor robbed Fernandinho in midfield, which freed 18-year-old Aarons to run through and slot the ball between Willy Caballero’s legs from a narrow angle on the right.
City received a further blow three minutes later when Silva was forced off after injuring his left knee in an early tangle with Taylor.
Pellegrini said that Silva’s knee injury would be assessed on Thursday, but played down the extent of a groin problem that saw Yaya Toure leave the fray during the second half, saying it was “nothing important”.
Silva’s replacement, the fit-again Samir Nasri, teed up Stevan Jovetic for a volley that Newcastle goalkeeper Rob Elliot had to parry and visiting captain Fabricio Coloccini then sliced the ball against his own post.
– Pelle sinks Stoke –
But Newcastle finished the first half strongly, with Paul Dummett testing Caballero from a corner and Adam Armstrong sliding the ball narrowly wide from Daryl Janmaat’s right-wing cross.
As Newcastle continued to press, with City left-back Aleksandar Kolarov fortunate not to concede a penalty for felling Gabriel Obertan, Pellegrini sent on Jesus Navas and Sergio Aguero.
But it was a Newcastle substitute who delivered the killer blow, with Sissoko skilfully dragging the ball away from Fernandinho and then bursting past Bacary Sagna before coolly stabbing home.
Taylor completed a memorable return by blocking on the line from Edin Dzeko in the 85th minute, as Newcastle secured a first ever win at the Etihad and sent the holders crashing out.
“It was a fairytale,” said Taylor. “It was a dream which all came true.”
Elsewhere, Graziano Pelle took his tally for the season to nine goals as in-form Southampton survived a late Stoke City rally to win 3-2 at the Britannia Stadium and set up a trip to third-tier Sheffield United.
The Italian curled Southampton ahead from 25 yards in the sixth minute and Shane Long made it 2-0, only for Steven Nzonzi to bring Stoke back into the game before Mame Biram Diouf headed in an 82nd-minute equaliser.
But after former Southampton player Peter Crouch had been sent off for a second bookable offence, Pelle swept home from the ensuing free-kick in the 88th minute to put Ronald Koeman’s side in the last eight.
In the evening’s other game, second-half goals from Erik Lamela and Harry Kane gave Tottenham a 2-0 victory at home to second-tier Brighton and Hove Albion.
Liverpool, who edged Swansea City 2-1 on Tuesday, will visit second-tier Bournemouth in the quarter-finals, while Chelsea were handed a trip to another Championship side, Derby County.