They were up against it for prolonged periods and needed extra time to complete the job but, eventually, Álvaro Negredo and Edin Dzeko scored the goals which earned a second-string Manchester City side a quarter-final place.

As Manuel Pellegrini smiled with evident relief, Alan Pardew looked disconsolate. Not only have Newcastle United failed to beat City in the last 15 attempts, but Pardew's class of 2013 have won only one of their past five games, leaving him on slightly uneasy terrain.

"It was a very close match but I'm very pleased," said Pellegrini. "It wasn't easy." His team have not convinced on the road this season and a largely impressive Newcastle began by highlighting City's defensive vulnerabilities. Shola Ameobi headed on for Papiss Cissé to nip between Dedryck Boyata and Joleon Lescott, extend a boot, and shoot narrowly wide. Minutes later another nodded flick-on from Ameobi precipitated a Cissé shot being blocked.

Neither strikers started Newcastle's 2-1 defeat at Sunderland last Sunday and, deployed in a 4-4-2 formation, as Pardew rejigged his recently preferred 4-3-3 system, both had points to prove.

Cheick Tioté should have simply been relieved not to be in a prison cell after receiving a suspended sentence following his conviction for possession of a forged Belgian driving licence on Monday. Rather generously, Pardew blamed it all on a "cultural misunderstanding" but with the Ivorian looking a midfielder reborn since assuming the captaincy from the injured Fabricio Coloccini, his manager would probably forgive him most things right now.

Tioté and the recalled, extremely assured, Vurnon Anita were certainly making Jack Rodwell look a bit stodgy and one-paced in City's central midfield as, gradually, inexorably, Newcastle forced the tempo and gained the upper hand.

Costel Pantilimon – keeping goal in place of the dropped Joe Hart – did well to repel Ameobi's volley but Pantilimon was beaten when Cissé's miscued volley flew across the face of goal only to be tapped home by Ameobi at the far post. No matter that this "goal" was disallowed for offside, Pellegrini's defence had, once again, being bisected. "This was a very important game for Costel, he's a very good keeper," said Pellegrini, who declined to offer Hart any reassurance but said he has still to decide whether Pantilimon will keep the place.

City were not enjoying the way Pardew's players were pressing them and with James Milner – fortunately for Newcastle's vulnerable Mathieu Debuchy – initially experiencing one of those nights when he is all industry and little imagination or incision, Tim Krul was strangely under-employed. Even so, home fears of coming undone on the break were heightened when Micah Richards slalomed forward, dodging all-comers, before shooting wide.

Then Tioté was booked for a typically rash foul from behind on the substitute Negredo, thereby ensuring the Ivorian needed to watch his second-half step. Tioté's latest yellow card also served to heighten Newcastle fears that his team-mates might struggle to maintain the intensity and ferocity of their first-half performance.

Yet despite odd flashes of skill from Jesús Navas – whose influence on proceedings was growing – and Richards heading a Milner cross over the bar when he probably should have scored, Pellegrini's players were still not moving the ball forward fast enough to really hurt Newcastle.

It was no surprise when the still-struggling Rodwell was replaced by David Silva, although Ameobi's replacement by Yohan Cabaye raised a few eyebrows, many fans feeling Cissé should have been the man withdrawn. Belatedly City roused themselves, with their pressure almost paying off when Tim Krul just managed to stretch out a hand to divert Negredo's shot at the end of a slick exchange between Dzeko and Negredo, who delayed a fraction too long.

Early in extra time, a fine pass from Hatem Ben Arfa resulted in Pantilimon having to deal with Cissé although, wastefully, the Senegalese striker shot straight at him. In the 99th minute everything changed. Dzeko's beautifully weighted square pass found Negredo unmarked and, gratefully accepting the invitation, he shot low past Krul.

Newcastle fans began heading for the exits when Dzeko doubled City's lead following a clever interchange involving Silva and Milner. The latter's adroit pass enabled Dzeko to round the advancing Krul before rolling the ball into the empty net.

"It was disappointing not to score," Pardew said. "We put City in a difficult situation but just couldn't get our noses in front."