Chelsea remain in second spot, although they were made to sweat before recording a 4-3 win at bottom side Sunderland.
The Blues netted through Eden Hazard (36 and 62 minutes), Frank Lampard (17) and an own goal from Phil Bardsley (84) with Sunderland's goals coming from Jozy Altidore (14), John O'Shea (50) and Bardsley (86) as the Black Cats came up just short.
Champions Manchester United fell further adrift of the Barclays Premier League pacesetters after losing at home to Everton for the first time since 1992.
Bryan Oviedo's goal four minutes from time gave Everton victory over their former manager David Moyes' United and meant the top five teams in the Premier League all picked up wins on Wednesday evening.
Perhaps more crucially though, that result at Old Trafford, combined with leaders Arsenal's 2-0 win over Hull, means United are now 12 points adrift of top spot and their grip on the title is looking increasingly shaky.
Fifth-placed Everton may have recorded the result of the night, but the individual performance of the evening undoubtedly belongs to Luis Suarez after he single-handedly fired Liverpool to victory over Norwich.
He took just 35 minutes to complete his treble and become the first Premier League player to score three hat-tricks against the same club, having also achieved the feat against the Canaries at Carrow Road in the last two seasons.
The Uruguay international then added a fourth goal with a superb second-half free-kick as he took his tally to 13 goals in just eight league appearances for the Reds since returning to action from his ban.
Norwich pulled a goal back through Bradley Johnson but Liverpool completed a 5-1 win with Raheem Sterling netting late on.
Suarez's heroics were not enough to see fourth-placed Liverpool climb the table however, with top three Arsenal, Chelsea and Manchester City all picking up victories.
Arsenal remained four points clear at the summit as goals from Nicklas Bendtner, who opened the scoring after just two minutes in a rare Premier League start for the Gunners, and Mesut Ozil saw them beat Hull.
1 Arsenal 34 2 Chelsea 30 3 Man City 28 4 Liverpool 27 5 Everton 27 6 Tottenham 24 7 Newcastle 23 8 Southampton 22 9 Man Utd 22 10 A Villa 19 11 Swansea 18 12 Hull City 17 13 West Brom 15 14 Stoke City 14 15 Cardiff 14 16 Norwich 14 17 West Ham 13 18 Fulham 10 19 C Palace 10 20 Sunderland 8
Manchester City also had a nervy finish before beating West Brom 3-2 to stay within two points of Chelsea and a point clear of Liverpool and Everton.
In a game that started 15 minutes late due to traffic congestion, Yaya Toure's brace followed an early opener from Sergio Aguero and saw City cruising at 3-0.
However, they had to survive a late scare as West Brom pulled two goals back in the final five minutes through Costel Pantilimon's own goal and a Victor Anichebe's strike.
Under-pressure Tottenham manager Andre Villas-Boas will be relieved man after seeing his side fight back from a goal down to beat Fulham 2-1.
Ashkan Dejagah gave Fulham a 57th-minute lead in new boss Rene Meulensteen's first game in charge, but goals from Vlad Chiriches (73) and substitute Lewis Holtby (82) saw Tottenham battle back for their first league win in five.
Southampton's recent struggles continued as they slumped to a third successive loss after going down 3-2 at home to Aston Villa.
Saints twice equalised, Jay Rodriguez (48) and Pablo Osvaldo (69) cancelling out efforts from Gabriel Agbonlahor (15) and Libor Kozak (64), but Villa would not be denied as Fabian Delph slotted home an 80th-minute winner.
In Wednesday's other games, Swansea beat Newcastle 3-0 with goals from Nathan Dyer (45), a Mathieu Debuchy own goal (66) and Jonjo Shelvey (81) while Stoke and Cardiff shared a goalless draw.