David Moyes warned his players their survival mission is not yet complete after four-goal Michail Antonio fired them to the brink of safety.
Victory at Norwich lifted West Ham six points clear of third-bottom Bournemouth who have one game in hand.
West Ham’s next game is a huge one against fourth-bottom Watford on Friday, with both sides locked on 34 points with three matches left.
Moyes said: ‘We are in a position where we have our noses in front and we have to make sure we do our job to remain a Premier League team.