Manchester City's Raheem Sterling grabbed his fifth Premier League hat-trick in a 4-0 win over Norwich City at Carrow Road on Saturday as the champion extended its lead at the top to 12 points.

Sterling missed a late penalty but notched a perfect hat-trick with goals from his right foot, head and left foot as a dominant City extended its unbeaten run in all competitions to 12 games, which include only one draw.

"You're not going to score everything that goes your way but keep shooting and the goals will come," Sterling, City's top scorer this season with 10 league goals, told  Sky Sports .

"To be a top team the challenge is to keep winning every three days."

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Norwich made a lively start with Grant Hanley going close to giving the home side a deserved lead but he saw his header come off the post, while Milo Rashica's magical run through midfield was stopped in its tracks by a Ruben Dias foul.

But the visitor finally broke the deadlock when Max Aarons failed to clear Kyle Walker's cross and Sterling picked up the ball, dribbled into the box and curled a right-footed shot past the outstretched arm of the keeper Angus Gunn.

Phil Foden doubled the lead just after the restart when he bundled the ball over the line after it pin-balled in the box, with the Goal Decision System awarding the goal after it was cleared off the line.

With a Champions League knockout tie against Portuguese side Sporting to come on Tuesday, City took its foot off the gas and enjoyed long spells of possession.

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But in the 70th minute, Dias headed Foden's cross across goal, where an unmarked Sterling nodded home for his second.

Once the three points were secured, City boss Pep Guardiola threw on teenagers James McAtee, Liam Delap and Kayky, with Delap winning a penalty when he was fouled by Hanley.

Sterling's final goal should have come from the spot but he saw his attempt saved before following up to complete his hat-trick with a tap-in.

Second-placed Liverpool has two games in hand and Guardiola was wary of the threat they posed.

"(We need) a lot of points. We know what rival we have, the closest one is Liverpool," he said.

"They won't drop many points for the quality they have. It's the best squad they have in the last decade. We'll have to win a lot of games."