Manchester United made it four wins in a row in all competitions after defeating West Ham United, and Newcastle United maintained their push for UEFA Champions League qualification with a comfortable victory at Crystal Palace.
Caretaker West Brom manager Keith Downing secured a point at home to Hull City, Sunderland were held at home by Norwich City and Stoke City got the better of Aston Villa.
Luis Suarez celebrated signing a new contract by scoring twice and setting up the other as Liverpool beat Cardiff City 3-1 at Anfield.
The home side made the breakthrough on 25 minutes when Suarez netted his 18th Premier League goal of the season after volleying Jordan Henderson's chipped ball past David Marshall.
Liverpool grabbed a second goal on 42 minutes when Henderson sent Suarez racing clear on goal with a superb pass and the Uruguayan unselfishly teed up Raheem Sterling to stroke the ball home from close range.
Things got even better for Liverpool on the stroke of half-time when Henderson found Suarez on the edge of the box with a clever back-heel and the in-form striker curled his shot into the far corner.
Cardiff pulled a goal back just before the hour mark when Jordon Mutch found himself unmarked from Peter Whittingham's cross to head home past Simon Mignolet.
Manchester City threw away a two-goal lead before regrouping to beat Fulham 4-2 at Craven Cottage to post a seventh win in eight games in all competitions.
David Silva struck the crossbar early on for City before the visitors took the lead on 23 minutes when Yaya Toure curled another excellent free-kick over the wall and off the underside of the bar.
The lead was doubled two minutes before half-time when Martin Demichelis' header was pushed out by Maarten Stekelenburg and City skipper Vincent Kompany stabbed home the rebound for his first goal of the season.
Fulham got themselves back in the game five minutes after half-time when Adel Taarabt got down the left and, with City's defence hopelessly exposed, crossed for the unmarked Kieran Richardson to score from about ten yards out.
With 20 minutes to go, Fulham drew level in comical circumstances when Sascha Riether played in a low cross and Kompany, under no pressure on the edge of the six-yard box, sliced his clearance into the air and the ball crossed the line after coming back off the post.
But City got their skipper out of jail on 78 minutes when Silva's pass released Jesus Navas on the right and the substitute drilled a low shot through the legs of Stekelenburg.
City made certain of the win by scoring a fourth goal on 83 minutes when Fulham failed to cut out Alvaro Negredo's brilliant pass with the outside of his left foot and James Milner steered his shot past Stekelenburg.
It was a day of notable goals as Manchester United avoided a third straight league defeat at Old Trafford courtesy of a 3-1 triumph over West Ham United.
The Red Devils took the lead on 26 minutes when Welbeck's clever flick released Wayne Rooney, who played his fellow England striker back in to score his first goal at Old Trafford since October 2012.
The champions increased their advantage 10 minutes later when Welbeck turned provider to slip in Januzaj, whose clever dummy deceived James Collins before the young winger flashed his shot beyond Adrian.
United added a third on 72 minutes when Rooney laid the ball off for Ashley Young to rocket a shot into the top corner for his first Premier League goal since May 2012.
But West Ham responded with a goal on 81 minutes when substitute Alexander Buttner played Carlton Cole onside and the striker ran through before rolling his shot through David de Gea's legs.
Alan Pardew enjoyed a winning return to Selhurst Park after the former Crystal Palace midfielder saw his Newcastle United side ease to a 3-0 success.
Newcastle were in front on 25 minutes when Moussa Sissoko did well down the right before pulling the ball back for Yohan Cabaye, whose shot took a deflection on its way past a wrong-footed Julian Speroni.
There was far greater fortune about Newcastle's second goal on 39 minutes when Mathieu Debuchy whipped in a cross from the right and, under little pressure, Danny Gabbidon diverted the ball inside the far post.
The Magpies made it 3-0 with four minutes left when Palace substitute Jonathan Parr tripped Shola Ameobi and Hatem Ben Arfa hammered home the penalty.
Matej Vydra scored his first goal for West Brom to salvage a 1-1 draw with Hull City in the first game at The Hawthorns since Steve Clarke's sacking.
West Brom fell behind on 28 minutes when Hull launched a counter-attack from the corner of their own penalty area which ended with Danny Graham sliding in Jake Livermore to finish low past Ben Foster, who was making his first appearance in four months.
The hosts poached an equaliser with four minutes to go when Shane Long and Zoltan Gera combined to set up substitute Vydra for his first goal since arriving on loan in the summer.
Stoke moved up to tenth in the table after Peter Crouch scored a 70th minute winner in a 2-1 victory over Aston Villa at the Britannia Stadium.
The Potters took the lead on 51 minutes with a goal which bore the hallmarks of former manager Tony Pulis as Crouch knocked down a deep, angled free-kick and Charlie Adam brought the ball under control before finishing past Brad Guzan.
But Stoke gifted Villa an equaliser 15 minutes later when Guzan's long clearance dropped to Erik Pieters and the left-back's poor header back to keeper Asmir Begovic was seized upon by Libor Kozak to flick home.
Yet Stoke were back in front four minutes later when Geoff Cameron's cross from the right was not cut out by Guzan and the ball possibly hit Crouch's arm before the striker scored into an empty net.
Wes Brown was sent off in stoppage time as Sunderland drew 0-0 with Norwich at the Stadium of Light to go into the Christmas period four points from safety.
Experienced defender Brown, who was harshly sent off at Stoke recently, again appeared slightly unlucky when he was shown a straight red card for a challenge on Ricky van Wolfswinkel.