The Spaniard rounded off an excellent team move to give Manuel Pellegrini's men the lead on 38 minutes with the Argentina international adding a second in stoppage time.
Silva raced onto Edin Dzeko's brilliant back-heel pass to fire clinically beyond Tim Krul on 38 minutes to give Manuel Pellegrini's men a narrow lead they never relinquished.
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Inspired by marquee summer signing Remy Cabella, Newcastle threatened an equalizer on several occasions during a tense second half, with substitute Ayoze Perez almost scoring within seconds of his arrival and Moussa Sissoko firing over late.
However, Sergio Aguero made the points safe in stoppage time, the substitute sweeping home from close range after Krul had saved his initial shot.
The champions began impressively. Some crisp passing ending with Dzeko's poked volley being kept out by goalkeeper Tim Krul following a lovely chipped Stevan Jovetic pass.
That set the tone for a dominant start, Samir Nasri stinging the hands of Krul with a half-volley from range.
Yet Newcastle gradually began to find its rhythm amid an emotional atmosphere that saw tributes both before and during the first half to remember supporters Liam Sweeney and John Alder, who lost their lives in the Malaysia Airlines flight MH17 crash.
New signing Cabella was bright for the home side, chipping just over the crossbar. However, he and his teammates could do little as City took the lead with a stunning goal in the 38th minute.
A searching ball forward found Dzeko, whose superb back-heel left Silva with the simplest of finishes.
Newcastle responded well after halftime, a deep corner finding Gouffran - whose effort drew a smart save from Joe Hart in the Manchester City goal.
The host's industry continued, too, with Paul Dummett heading just over in between three Jovetic half-chances.
The best of those came when the forward was denied by a superb Fabricio Coloccini block as City threatened a second goal.
Jovetic also was instrumental in City's next opening, sending over a clever pass that Dzeko headed narrowly over with 27 minutes left.
Suddenly back on top, the visitors continued to press forward, with Yaya Toure's free kick narrowly missing the target late.
That effort preceded a spell of home pressure as Alan Pardew's side did everything in its power to get back into the game, substitute Perez seeing an effort deflect agonizingly wide.
Newcastle then spurned an even better chance, as Sissoko blazed over from just outside the area.
And City made the home side pay, Aguero - on as an 83rd-minute replacement for Dzeko, much to the delight of the City fans - curling home after his initial effort was saved by Krul.