Sam Allardyce believes Sunderland now have a great chance of staying up after their "massive" 3-0 win at relegation rivals Norwich.
Fabio Borini's first-half penalty and second-half strikes from Jermain Defoe and Duncan Watmore left the Black Cats just a point from City, and safety, with a game in hand.
"It's a huge moment for us, to come here and try to win this game," said Sunderland boss Allardyce.
"Dealing with the pressure paid off. That was the key element to our victory because of the position we are in and because we were away from home.
"Our clinical finishing at the right time put the game to bed and our defending was superb. Everything was right. It's a massive result and it gives us a lot more hope
"If we'd lost we'd have been seven points behind. Now it's only one point, a better goal difference and a game in hand. If we can pick up some points next week, then we can rush in and see how everyone else has done."