In a game short of action, Manuel Pellegrini’s men soaked up increased pressure from the hosts in the first-half to eventually see them leave with victory after goals from Alvaro Negredo and Edin Dzeko.
Pellegrini made 10 changes to the side that lost to Chelsea in the Premier League last weekend and that showed early on as Newcastle enjoyed the better of possession and looked the more likely to open the scoring.
But Costel Pantilimon, standing in for Joe Hart, made a number of crucial saves to ensure the hosts were not out of sight by the interval.
Papiss Cisse wasted two good chances before Shola Ameobi had a goal ruled out for offside after he tapped in Cisse’s miscued shot across goal. City, on the other hand, lost Stevan Jovetic in the opening stages to a calf injury and Alvaro Negredo was introduced in his place, but they still lacked any real threat in front of goal without the rested Sergio Aguero.
Micah Richards headed over early in the second-half and James Milner missed a sitter after Tim Krul found himself at sixes and sevens with a through ball.
Spanish midfielder David Silva came on mid-way through the second half and immediately gave City the cutting edge they so desperately needed, but Negredo spurned two good chances as the game headed towards extra-time.
The first-half of extra-time saw much of the same from both sides, with Cisse wasting another golden chance to give the hosts the lead as Pantilimon saved expertly after Hatem Ben Arfa’s superb ball.
City eventually found the breakthrough in the 99th minute, though, after Negredo showed why City splashed out £22million on him. Dzeko worked his way down the left of the Newcastle penalty area before squaring goalwards to Negredo, whose movement to lose defender Mapou Yanga-Mbiwa was impressive, and he slotted past Krul with ease.
And City doubled their lead just six minutes later, putting the game out of sight for Newcastle. Milner and Silva’s impressive link-up play led to Dzeko easily rounding Krul to slide home.
The defeat will have been a hard one to take for Magpies boss Pardew who will have been impressed by the way his side reacted to their loss to arch-rivals Sunderland at the weekend. His major worry will be the lack of goals coming from his strikers, particularly after the likes of Cisse spurned several chances throughout the game.
Meanwhile, Pellegrini was delighted with his side’s patience to win the game and insists City deserved to go through despite having to rely on Pantilimon to keep them in the match on various occasions.
City will now travel to the King Power Stadium to face Leicester City in Round 5.