Fulham hit back from 2-0 down to draw level, but City moved up a gear to seal the three points and stay firmly on the heels of Premier League leaders Liverpool.
Milner scored City's fourth and he said: "When they got two back we really had to dig in.
"To come back again and show the character to kick on and get the two goals was pleasing.
"It's a good start to the festive period. A lot of games are coming up, but if we can keep that desire and that will to win up, that will get you most of the way."
Milner converted a delightful cross from Alvaro Negredo to seal victory and kill off any Fulham hopes of a reply.
"He's got great ability," said Milner of Negredo. "He doesn't really need to use his right foot, his left foot's that good. He can do anything with it.
"It was all made in the ball really. I just had to make sure I got a bit of contact on it. I was pleased to see it go in, it just gave us that cushion for the last few minutes."
It was City's third away win from nine games this season, a statistic which contrasts starkly with their 100 per cent home record from eight matches.
That perfect record will be tested on Thursday against Liverpool and the rampaging Luis Suarez.