Goals from substitute Alvaro Negrado and Edin Dzeko in the first-half of extra-time saved City from an upset after a rather disjointed performance in the first 90 minutes of the match.
After suffering a disappointing 2-1 defeat against title rivals Chelsea at the weekend, City manager Manuel Pellegrini made 10 changes to his side with Javi Garcia the only survivor.
As expected Joe Hart was dropped to the bench as Costel Pantilimon replaced the England goalkeeper.
Alan Pardew also made changes to his side which lost 2-1 to neighbours Sunderland as he brought in five new faces including Shola Ameobi, who replaced Loic Remy, and Yohan Cabaye was also dropped to the bench.
It was the hosts who made the brighter start to the match with Papiss Cisse, Ameobi and Vurnon Anita all going close to breaking the deadlock in the first-half.
Newcastle had their first opportunity on eight minutes when Ameobi was highest to Tim Krul's goal-kick and his header found Cisse whose flick just went narrowly wide.
An injury to Stevan Jovetic forced Pellegrini into an early substitution as Negrado was introduced on 10 minutes.
It was Ameobi who was first to test what Pantilimon was all about when he fired a low half-volley across the Romanian's goal and he saved well to push the ball around the post.
And it was the Newcastle veteran who thought he had finally broken the deadlock on 31 minutes when he tapped in at the back post after Cisse scuffed his shot but the linesman ruled the goal out for offside.
A minute later the home side went close again when Anita somehow shot narrowly wide after the ball had fell wonderfully for the midfielder on the edge of the area.
Despite a poor showing in the first-half, Pellegrini chose not to make any changes at the break and it was an improved display from City in the second period.
James Milner had City’s first real opportunity on 62 minutes when Krul – who rushed out of his box to clear - was dispossessed by Jesus Navas but the Englishman saw his effort flash narrowly over the bar from distance.
With Newcastle no longer dominating proceedings, Pardew looked to the bench to freshen things up as Cabaye and Hatem Ben Arfa replaced Ameobi and Paul Dummet but still the home side – who have never won the League Cup – could not find the net.
Negredo gave an indication of things to come when he forced Krul into a good save as he attempted to lob the goalkeeper from close range on 77 minutes.
The referee brought a rather drab 90 minutes to a close and the game entered extra-time, much to the displeasure of both sides.
Although the added time was to be to City’s advantage, they came very close to trailing the game on 91 minutes when substitute Ben Arfa found Cisse with a wonderful lobbed pass to put the out-of-form striker in the clear and his goal drought continued when the Romanian goalkeeper rushed out of goal to make a fantastic save.
But City made the hosts pay for their inaccurate finishing on 99 minutes through Negrado when he was in position to tap home a squared ball from his forward partner Dzeko.
And the big Bosnian sealed the game six minutes later when he rounded Krul after latching onto Milner's through ball to set up a quarter-final trip to Leicester.
- Sports & Recreation
- Shola Ameobi
- Manuel Pellegrini
- Papiss Cisse
- Yohan Cabaye
- Tim Krul
- Alan Pardew