Foden, who had been sidelined earlier this season with a nagging foot injury, put City ahead in the 15th minute with his fourth goal in three games in all competitions.
The midfielder showed remarkable control, weaving through four Newcastle defenders and into the box before his angled shot glanced off the outstretched foot of Sven Botman and past keeper Nick Pope. Silva came off the bench in the 65th minute and the Portugal international scored two minutes later with a sharp finish past Pope after a flick from Erling Haaland.
It was another blow to Newcastle’s top-four hopes with Eddie Howe’s side, who lost 2-0 to Manchester United in last week’s League Cup final, having recorded just win in their last eight league games.