Yohan Cabaye gave the Magpies a 16th-minute lead that was doubled in the 33rd when Loic Remy netted.
The Hammers pulled one back on the stroke of half-time courtesy of an own goal by Michael Williamson, but Cabaye's fifth goal in his last seven matches late on sealed the home side's fate.
Liverpool battled back for a 2-2 draw with Aston Villa.
Liverpool came from two goals down to earn a 2-2 draw with Aston Villa in an entertaining clash at Anfield in Saturday's final Barclays Premier League match.
Villa raced into a deserved 2-0 lead thanks to goals from Andreas Weimann and Christian Benteke, but Daniel Sturridge pulled a goal back right on the stroke of half-time to give the home side hope.
Liverpool won a penalty early in the second half as Luis Suarez went down in the box under a challenge from Brad Guzan and Steven Gerrard scored from the spot.
The home side pushed for a winner, but the Villa defence held firm as Liverpool were held to a draw for the first time this season at Anfield.
Two goals in five second-half minutes from Santi Cazorla ensured Arsenal retained their grip on top spot.
Following a wobble in December, Arsene Wenger's side have won their last five league matches, with Fulham their latest victims as the Cottagers were beaten 2-0 at the Emirates Stadium.
Liverpool 2 - 2 A Villa
C Palace 1 - 0 Stoke City
Norwich 1 - 0 Hull City
West Ham 1 - 3 Newcastle
Man City 4 - 2 Cardiff
Arsenal 2 - 0 Fulham
Sunderland 2 - 2 Southampton
In front of their own fans the Gunners typically dominated play, but had to wait until the 57th minute for Cazorla to sweep home the first of his brace with his right foot.
Just past the hour mark and Spaniard Cazorla, with only two goals to his name ahead of this game, doubled his tally for the season, this time with a superb let-foot drive from outside the area.
Manchester City remain hot on Arsenal's heels after another victory at the Etihad Stadium, this time despatching Cardiff 4-2.
It took just 14 minutes for Edin Dzeko to open the scoring, a close-range left-foot shot making it 100 goals for Manuel Pellegrini's side in all competitions this season.
Yet the hosts did not have it all their own way in the opening exchanges as Craig Noone hauled Cardiff level just before the half-hour mark.
The visitors' joy, however, was shortlived as Jesus Navas fired the home side back in front in the 33rd minute.
That was followed by a goal apiece from Yaya Toure and Sergio Aguero in under three minutes in the second half before Fraizer Campbell netted a late consolation.
1 Arsenal 51
2 Man City 50
3 Chelsea 46
4 Liverpool 43
5 Everton 41
6 Tottenham 40
7 Man Utd 37
8 Newcastle 36
9 Southampton 31
10 A Villa 24
11 Hull City 23
12 Norwich 23
13 Stoke City 22
14 Swansea 21
15 West Brom 21
16 C Palace 20
17 Fulham 19
18 West Ham 18
19 Sunderland 18
20 Cardiff 18
At Selhurst Park, Tony Pulis was smiling as Crystal Palace beat former club Stoke 1-0.
Pulis, who left Stoke last May before taking up the reins at Palace in November, saw Jason Puncheon strike the 51st-minute goal that has lifted his side off the foot of the table.
Norwich defender Ryan Bennett scored his first goal for nine months as the Canaries defeated Hull 1-0 at Carrow Road.
Despite club-record signing Nikica Jelavic playing for Hull, it was Bennett who broke the stalemate in the 87th minute with a fine header to a cross from Robert Snodgrass.
Further misery followed for the visitors when Tom Huddlestone was dismissed two minutes later for his second bookable offence.
In the early kick-off at the Stadium of Light, Sunderland came from two goals down to earn a point from a 2-2 draw with Southampton.
Jay Rodriguez arrowed home a stunning strike from 22 yards after just four minutes for the Saints before Dejan Lovren doubled the visitors' advantage on the volley just after the half hour.
Crucially for Gus Poyet's side they managed to reduce the arrears a minute later courtesy of Fabio Borini's fourth goal for the club in his season-long loan from Liverpool.
When Adam Johnson equalised with 19 minutes remaining the momentum was then with Sunderland, although they failed to force home a winner to lift them out of the bottom three.