United boss Alan Pardew fielded an extremely inexperienced side, featuring six changes from the weekend league win at Tottenham, but he was rewarded with an energetic and committed display from his youthful team.
This was epitomised by teenage forward Rolando Aarons, who showed raw pace to go past Eliaquim Mangala and unexpected poise to finish low past Willy Caballero from a tight angle to open the scoring in just the sixth minute.
The away side had to weather plenty of pressure and survived a scare when Fabricio Collocini sliced a clearance on to the frame of his own goal in the first half.
But they strengthened their grip on the game with 15 minutes remaining when substitute Moussa Sissoko broke into the box and clipped a superb shot into the far corner of the goal before holding out for a famous triumph.
The win continues Newcastle’s recent rejuvination under Pardew, who has now overseen three successive victories, having previously managed just two in the previous nine, both in the League Cup.
In contrast, it is worrying times for City, who threw away a two-goal lead to draw against CSKA Moscow in the Champions League and lost 2-1 at West Ham in the Premier League in their two games prior to this defeat.
City boss Manuel Pellegrini fielded a strong team for Wednesday’s tie, but despite their vastly superior possession they were unable to break down the Newcastle defence.
The home side certainly had their chances to score.
Stefan Jovetic should have netted with a shot at the back post from a Samir Nasri cross but was denied by a superb save from Rob Elliot, while Edin Dzeko had an even better chance late in the game with a shot from point-blank range that was blocked by the diving Ryan Taylor on the line.
But what characterised City’s performance was a lack of speed, a scarcity of penetration and, most worryingly, a lack of ideas in the final third.
It could have been even worse for them had Caballero not superbly saved a Paul Dummett volley from a corner and the referee not waved away the protests for what looked like a clear penalty for a foul on Gabriel Obertan in the box by Aleksandar Kolarov.
Newcastle’s reward for the victory is an away trip to Tottenham in the last eight.