"What we showed in the last few games is that we will never give up".
The Irons, who appeared more organised than they have done in recent matches, finally got the goal they deserved when Angelo Ogbonna headed home from an Aaron Cresswell cross and scored his first in the Premier League just before the break.
'The second half with Gabriel Jesus inside we had more players in the box.
But City didn't panic and after Otamendi equalized on 57 minutes, they poured forward and a stunning pass from Kevin de Bruyne set up Silva to volley in the victor.
It hasn't always been plain sailing for Pep Guardiola's side however, as on four occasions (Bournemouth, Huddersfield, Southampton, West Ham) they've had to come back from a goal down, and on four occasions they've relied on late goals to secure all three points (Bournemouth, Huddersfield, Southampton, West Ham).
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The goalkeeper got a rare start for the Hammers as Joe Hart was unavailable to play against his parent club.
Boss Guardiola smiled: "I heard about Fergie time. We want to win the derby but we are taking it each game at a time". It was massive. They played 10 players inside the box, it was nearly impossible.
"We spoke a lot about defending set pieces but they are taller", Guardiola added.
Guardiola - who admitted Sergio Aguero's form has dipped significantly since his vehicle crash in Amsterdam - would not be drawn on Paul Pogba publicly wishing injuries on his City rivals.
West Ham created the better chances than their opponents in the opening 45 minutes and had the opportunity to make Citizens pay for an apparent arrogance, with Michail Antonio wasting a glorious chance at the back post inside the first ten minutes. "We played against a really good side and I thought for long periods we frustrated them". "But we have players like David Silva in the team, so we knew if we kept going we'd get our chances".