Newcastle competed well in an absorbing Premier League encounter but fell behind in the 38th minute on Sunday when David Silva slotted home a calm finish from Edin Dzeko's exquisite back-heel.
Man City had to defend for long periods in the second half and Newcastle almost grabbed an equaliser when Ayoze Perez’s shot was deflected just wide.
However, City made sure of victory in stoppage-time as substitute Sergio Aguero fired in on the rebound after his initial shot had been saved.
The afternoon started with captains Fabricio Coloccini and Vincent Kompany, along with former Sunderland goalkeeper Jimmy Montgomery, laying wreaths on the centre circle as they were joined by relatives of fans John Alder and Liam Sweeney, who died on Malaysia Airlines Flight MH17.
But while City played their full part in an emotional start to the afternoon, they ripped into their hosts from the off and might have established a commanding lead within the opening 11 minutes.
Goalkeeper Tim Krul had to be at his most alert to keep out Dzeko's close-range second-minute effort after Stevan Jovetic had played him in over the top with a delicately lofted pass, and the Dutchman was in action once again nine minutes later.
Samir Nasri and Aleksandar Kolarov played a long-range one-two before the Frenchman teed himself up to unleash a rasping drive which Krul had to dive full-length to turn away.
But as they warmed to their task, the Magpies started to make an impact.
Coloccini and central defensive partner Mike Williamson managed to get to grips with Dzeko and Jovetic to allow the men in front of them to prosper, although, while there were flashes from Remy Cabella and Emmanuel Riviere and a series of surging runs from Moussa Sissoko, there was little of note to trouble Joe Hart.
Cabella drifted a chipped 16th-minute effort over Hart's crossbar and Riviere, who showed plenty of endeavour, but slightly less composure, scuffed wide from distance and blazed across goal when he might have done better.
At the other end, Williamson denied Jovetic with a perfectly timed block, but the respite was temporary and City took the lead with seven minutes of the half remaining.
Coloccini and Williamson were both drawn to Dzeko as he chased down a long ball, and both were left stranded when he cleverly back-heeled it between them for Silva to exploit the space and fire left-footed past Krul.
Newcastle responded in determined fashion immediately after the restart with Yoan Gouffran seeing two shots blocked in quick succession after Jack Colback's 50th-minute corner reached him beyond the far post, and Cabella scooped over under pressure from Sissoko's pass.
Full-back Paul Dummett headed over after reaching Colback's corner ahead of Hart, but it took a good block by Coloccini to prevent Jovetic from extending the visitors' lead on the hour.
Dzeko headed onto the roof of Krul's net 25 minutes from time and Yaya Toure, who endured one of his quieter afternoons, floated a free-kick just over eight minutes later.
The Magpies threw caution to the wind as time ran down and substitute Perez saw a shot deflected just wide of the far post before Sissoko blazed wastefully over at the death.
But substitute Aguero wrapped up the win in stoppage time when, after Krul had blocked his initial effort, he stabbed the rebound home from close range.