Norwich and Newcastle both had a man sent off at the end of a bad-tempered 0-0 draw at Carrow Road.
Striker Loic Remy and Norwich midfielder Bradley Johnson were each shown a red card by referee Chris Foy after pushing and then squaring up head-to-head on the touchline.
It was a frustrating end to the night for the visitors, who travelled to Norfolk without key midfielder Yohan Cabaye, set for a £20million switch to Paris St Germain, but should have left with all three points after dominating the first half and hitting the woodwork three times.
Liverpool striker Daniel Sturridge scored two and missed a penalty but it was captain Steven Gerrard who dictated the tone of the 222nd Merseyside derby as Everton were thrashed 4-0 at Anfield.
The England skipper had endured a miserable 45 minutes on his last appearance on this ground against Aston Villa 10 days ago but he rarely does not turn up for a cross-city clash.
He duly led from the front and his influence plus Liverpool's superior firepower meant the Toffees never stood a chance.
1 Arsenal 52
2 Man City 50
3 Chelsea 49
4 Liverpool 46
5 Tottenham 43
6 Everton 42
7 Man Utd 40
8 Newcastle 37
9 Southampton 32
10 Swansea 24
11 A Villa 24
12 Norwich 24
13 Hull City 23
14 C Palace 23
15 West Brom 22
16 Stoke City 22
17 Fulham 19
18 West Ham 18
19 Sunderland 18
20 Cardiff 18
Gerrard's header opened the scoring in the 21st minute and was followed by Sturridge's two in quick succession with Luis Suarez scoring his 23rd of the season just after half-time.
Suarez and Sturridge now have 36 Premier League goals between them and remain the most crucial factor in Liverpool regaining their place among Europe's elite.
They helped lift some of the gathering gloom over the club's failure to strengthen in the January transfer window with exactly the sort of performance to give a much-needed shot in the arm to their Champions League qualification challenge.
It was not supposed to be like this for Everton as, following the 3-3 draw at Goodison Park in November and with their rivals in the top four by only a point, this was billed as the closest derby for years and the Toffees' best chance of ending their 14-year run without a win at Anfield.
Juan Mata enjoyed a winning start to life at Manchester United as Robin van Persie and Ashley Young scored the goals that defeated Cardiff 2-0 at Old Trafford.
Mata completed 83 minutes of his debut following his club-record £37.1million move from Chelsea.
The midfielder made an immediate impact, sparking the move that led to Van Persie's sixth-minute opener.
And while manager David Moyes will doubtless expect an even greater contribution as Mata gets used to his new surroundings, it is evident United's supporters have been uplifted by the 25-year-old's arrival as they offered a standing ovation when he was replaced by Adnan Januzaj.
By then, Young had belted in an excellent second to ensure the highpoint of Ole Gunnar Solskjaer's Old Trafford return was the reception he received from the home fans as his side remained at the foot of the Premier League.
Liverpool 4 - 0 Everton
C Palace 1 - 0 Hull City
Man Utd 2 - 0 Cardiff
Norwich 0 - 0 Newcastle
Swansea 2 - 0 Fulham
Southampto 2 - 2 Arsenal
Arsenal failed to stretch their advantage at the top of the Premier League as Southampton secured a deserved 2-2 draw in a frenetic encounter at St Mary's.
Kicking off 24 hours before their closest rivals, Arsene Wenger's side were unable to keep up the pressure on Manchester City and Chelsea as they blew what had been an impressive second-half comeback.
They were forced to settle for a point in a clash that ended a five-match winning streak, which means they could be usurped at the top of the standings on Wednesday.
Deflected efforts from Jonjo Shelvey and Chico Flores gave Swansea their first win in nine Premier League matches to ease their relegation fears as they claimed a 2-0 victory over fellow strugglers Fulham.
Shelvey put the hosts ahead in the 61st minute when his shot from the edge of the box struck Wilfried Bony and Brede Hangeland to beat a helpless Maarten Stekelenburg.
Flores' near-post header, which flicked in off Dimitar Berbatov, sealed the 2-0 win, just the third on home turf this term, and moved Swansea up to 10th in the table.
Fulham failed to make the most of excellent first-half chances for Hangeland and Ashkan Dejagah as they slipped to a defeat which ensures they remain just a point above the drop zone.