Manchester United snapped a losing start to 2014 by ending their run of three straight defeats in three different competitions by beating Swansea at home in Saturday Night Football.
Everton lifted themselves into the UEFA Champions League places following a home win over Norwich City and Tottenham Hotspur remain in the hunt for the top four after disposing of Crystal Palace.
Keith Downing will hand over the West Bromwich Albion reins on a losing note after Southampton enjoyed a first home victory in almost two months.
Eden Hazard and Fernando Torres struck as Chelsea overcame Hull City 2-0 at the KC Stadium to go top of the Premier League.
Chelsea made the vital breakthrough on 56 minutes when David Luiz and Ashley Cole played in Hazard, who cut inside from the left and drilled a powerful finish into the bottom corner.
Torres then put the result beyond any doubt on 87 minutes when he had enough pace to jockey Alex Bruce out of position as he bore down on goal before finishing crisply past Allan McGregor.
Ole Gunnar Solskjaer's first Premier League match as Cardiff manager ended in defeat as West Ham posted a 2-0 win in south Wales, despite being reduced to 10 men with 20 minutes to go.
West Ham lost Guy Demel to injury after just 10 minutes when the full-back was caught in the face by team-mate Roger Johnson and was then taken to hospital to be assessed.
Cardiff thought they had taken the lead just after the half-hour mark when Kim Bo-kyung's deflected shot came back off the bar, but did not bounce over the line before Fraizer Campbell was penalised for bundling West Ham keeper Adrian over the line.
The visitors then took the lead three minutes before half-time when Matt Jarvis played in a first-time cross from the right and Carlton Cole finished past David Marshall.
The Hammers' cause suffered a blow on 72 minutes when fit-again defender James Tomkins was shown a second yellow card after catching Campbell.
But Mark Noble drilled home an injury-time second to make the game safe for West Ham, who move out of the relegation zone and drop their opponents into the bottom three.
Adam Johnson scored the first hat-trick of his career as Sunderland moved up a spot to 19th after thrashing fellow strugglers Fulham 4-1 at Craven Cottage.
Sunderland went ahead on 29 minutes when Johnson curled a left-footed free-kick over the wall towards the top corner, but David Stockdale was unable to keep it out after getting both hands to the ball.
The Black Cats increased their advantage four minutes before the break when Johnson's low free-kick into the box teed up Ki Sung-yueng and the South Korean's shot took a deflection off Philippe Senderos on its way past Stockdale.
Fulham pulled a goal back seven minutes after half-time when Damien Duff whipped in a corner and Steve Sidwell stooped to head home after his run was not tracked.
But Sunderland reasserted on 69 minutes following a superb counter-attack as Ki and Jozy Altidore exchanged passes before the on-loan Swansea man's incisive pass set up Johnson to finish through Stockdale's legs.
Johnson completed his hat-trick five minutes from time when he sent Stockdale the wrong way from the penalty spot after Senderos brought down substitute Altidore with a half-hearted challenge.
Manchester United avenged last week's FA Cup third-round defeat by Swansea City with a 2-0 Premier League victory over Michael Laudrup's side at Old Trafford.
Adnan Januzaj struck the crossbar for United with an early free-kick, but it was Swansea who controlled possession in the first half without posing a major threat.
However, United scored the decisive first goal barely a minute into the second half when Antonio Valencia fired home the loose ball after Gerhard Tremmel had pushed out Shinji Kagawa's shot.
The second goal arrived on 59 minutes when Patrice Evra bundled the ball into the box and Danny Welbeck flicked a shot beyond Tremmel.
Everton moved back up to fourth spot in the standings after posting a comfortable 2-0 success over Norwich City at Goodison Park.
The Toffees took the lead midway through the first half when Romelu Lukaku laid the ball off to Gareth Barry and the midfielder was allowed to stride forward before arrowing a rising 25-yard shot beyond John Ruddy.
Norwich keeper Ruddy was again left grasping at air for Everton's second goal on 59 minutes when Kevin Mirallas curled a 25-yard free-kick up and over the wall.
Crystal Palace slipped to the foot of the table after suffering a 2-0 defeat at the hands of London rivals Tottenham at White Hart Lane as Jermain Defoe scored just a day after it was confirmed he will be joining Toronto FC.
Palace wasted a golden chance to take the lead on eight minutes when Mousa Dembele's clumsy challenge brought down Marouane Chamakh in the box, but Jason Puncheon's penalty was woeful as he fired high and wide into the stands.
Nabil Benteleb's curler came back off the post for Spurs before the hosts took the lead on 50 minutes when Emmanuel Adebayor flicked on a long ball and Christian Eriksen took a touch before crashing a shot past Julian Speroni.
Spurs went further ahead on 73 minutes when Aaron Lennon fed Defoe and, after the ball bounced kindly in the box, the substitute lifted his shot over Speroni.
New West Brom manager Pepe Mel watched from the stands as Adam Lallana's goal secured Southampton a 1-0 win at St Mary's.
Southampton made the breakthrough on 66 minutes when Gaston Ramirez dinked a pass into the path of Adam Lallana and the England international controlled the ball brilliantly before slotting a low right-footed shot past Ben Foster.