David Moyes is aiming to overtake Man Utd in the table after bouncing back from Thursday's heartbreak against Frankfurt.
The Hammers suffered elimination in the Europa League semi-final but responded with a 4-0 win against Norwich and now sit three points behind sixth-placed Man United having played a game less.
They were helped by Tim Krul who had a nightmare in goal for the Canaries and Moyes is delighted by the way they played, and more importantly by the victory.
Moyes said: "I think considering all the things that happened in midweek and how our emotions were, it was a really good result.
"I thought the team started very well and gave us a decent platform to go and work from.
"To say Thursday was a big blow wouldn't do it justice, how we feel. So to get us back today with that result was great credit to the players.
"We could've played better, could've scored more goals. But we got the job done and got three good points.
"Let's be fair, we've got Manchester City and Brighton to play, and Brighton have just beaten Manchester United, so that's why I thought today was really important.
"But we're back in it, back in there fighting and trying to be sixth or seventh with a bit of luck, and hopefully we can be back in Europe."
Krul was badly at fault for goals from Said Benrahma and Michail Antonio to leave his side 2-0 down after half an hour.
West Ham were three up by half-time thanks to Benrahma's second, and Manuel Lanzini added the fourth from the penalty spot after handball by Jacob Sorensen.
Jarrod Bowen set up the first three goals and is now the first West Ham player to register 10 goals and 10 assists in one season since Paolo Di Canio 22 years ago.
Canaries boss Dean Smith admitted Norwich's defending let them down badly again.
"We know we are in the Championship next season and if you give goals like that away and give teams a head start it's going to be tough," he said.
"Tim's our most experienced Premier League player, he knows when he's made a mistake and he'll hold his hands up.
"The third goal sums up where we were, where our minds are. You can feel sorry for yourselves but we didn't get any pressure on and the goal came from that."