Foden's fine run and deflected finish gave the champions the lead at the Etihad Stadium, before Silva's powerful effort made sure of the points for Pep Guardiola's side with 67 minutes gone.
The Magpies had their moments, however, with Sean Longstaff, Callum Wilson and Joelinton among those who saw chances come and go, with Eddie Howe's men ultimately unable to find a way back.
City fired an early warning when Ilkay Gundogan nodded Jack Grealish's cross just over but Howe's team, once they settled, looked a threat on the break. One such burst forward led to Anthony Gordon - on his full debut for the club - miscuing his shot as he closed in on goal from the left.
Quarter of an hour in, though, United fell behind. It was a superbly crafted opener, with Foden gliding into the box from the right flank, but the visitors could still feel a touch unfortunate as the England man's subsequent shot took a hefty deflection off Sven Botman on its way past the returning Nick Pope.
Sean Longstaff saw a shot blocked just in time by Nathan Ake as Newcastle looked to respond immediately while the prolific Erling Haaland glanced wide at the other end as chances fell to both sides. Perhaps the best opportunity since Foden's strike fell to Callum Wilson before the break, but he couldn't connect properly with Kieran Trippier's back-post knock-down in front of goal and City scrambled it clear.
The second half began with the champions in the ascendency but still a hint of sloppiness about both sides' play in the final third. A Grealish effort comfortably cleared Pope's crossbar in their first real attempt after the restart, while a swift break from Howe's charges resulted in Gordon cutting inside and shooting under pressure, but it was too high.
Howe then turned to his bench with just under half an hour remaining, with Alexander Isak, Allan Saint-Maximin and Joe Willock all introduced in a bid to pull themselves level. The hat-trick of changes almost brought an instant equaliser as, first, Joelinton failed to turn in a cross across the box and then Isak saw his shot repelled by Ake and then goalkeeper Ederson.
But while the Swedish forward's industry looked to be causing some concern for the City backline, with a quarter of the contest left United's task became more difficult, and it was a blow they couldn't recover from. Grealish cut in from the left once more and Haaland's flick into the path of Silva was gratefully received by the Portuguese international, who blasted home beyond Pope to seal the points.
The hosts could have had a third in the final five minutes when Foden's low strike was well saved by Pope down low to his right, but a third goal would have been harsh on Newcastle, who were left to rue their profligacy in front of goal.
