The Magpies showed eight changes to the side who lost 2-0 to Watford in the FA Cup fourth round at the weekend.
Meanwhile, Sergio Aguero, David Silva, Leroy Sane, Raheem Sterling and Aymeric Laporte all returned for City after not starting in the FA Cup win over Burnley.
And the recalled Aguero took a mere 24 seconds to make his mark, as Sterling crossed from the right, Silva got his head to the ball ahead of Martin Dubravka and Aguero was on hand to drive home the loose ball.
Aguero had the ball in the net again 18 minutes in, but a quickly-taken free-kick by Kevin de Bruyne was brought back by referee Paul Tierney, who showed the Belgian a yellow card.
The hosts responded, with Christian Atsu having a shot deflected away to safety by John Stones, while shortly before the break Fabian Schar did well to clear a Silva header away from close to the goal-line.
Early in the second half a Leroy Sane cross fizzed across the face of goal, with Sterling just unable to apply the finishing touch.
Dubravka then made a decent save to deny Silva as the visitors pushed for a second goal, with the Magpies finding it hard to make any headway at the other end of the pitch.
However, that all changed 24 minutes from time as City failed to deal with a cross, Isaac Hayden headed it back towards goal and Salomon Rondon managed to hook the ball home past the despairing dive of Ederson.
And, unbelievably, 12 minutes from time Fernandinho miscontrolled the ball inside his own area and his resulting lunge sent Sean Longstaff crashing to the turf.
Following a delay for a knock to Ederson, Matt Ritchie stepped forward and was able to squeeze his spot-kick home to give the hosts a 2-1 lead.
The Citizens poured forward in the closing minutes in an attempt to try and rescue something from the game, but were unable to find a way through and looked thoroughly dejected as the final whistle sounded.