Jose Mourinho's unbeaten Premier League record at Stamford Bridge continues, with the Portuguese coach having not tasted defeated in West London in 74 matches.
The loss also extended Everton's negative run away at Chelsea, having failed to win on any of their previous 19 visits.
Providing that he is awarded the goal, Chelsea skipper John Terry will have found the net on 35 occasions in the English top flight.
Arsenal 4-1 Sunderland
Prior to his brace, Olivier Giroud had not scored in his last five outings at the Emirates Stadium.
Staying with the goals theme, when Tomas Rosicky made it 3-0 to the home side, it was the Premier League's 700th goal of the season.
The visiting Black Cats have failed to win 10 of their 13 encounters away from the Stadium of Light.
Cardiff City 0-4 Hull City
January signing Nikica Jelavic scored his second and third goals for Hull since his arrival from Everton.
The Croatian's contribution went a long way to his manager Steve Bruce securing his 100th victory as a manager of a Premier League club.
After their latest home failure to score, the hosts have found the net just 12 times at the Cardiff City Stadium.
Manchester City 1-0 Stoke City
Ivorian midfielder Yaya Toure's goal was the 13th that he has scored so far this season.
His strike meant that City have scored just once in their last three Premier League matches.
As for Stoke, they have still just won one fixture away from the Britannia Stadium, having lost on 10 occasions.
West Bromwich Albion 1-1 Fulham
Pepe Mel was hired to reverse West Brom's ailing fortunes, but the Spaniard is yet to see the Baggies win during his six matches at the helm.
The draw was West Brom's 13th of the campaign, which is more than any of their peers have recorded.
Meanwhile, Fulham's Ashkan Dejagah scored his first goal away from Craven Cottage.
West Ham United 3-1 Southampton
West Ham striker Carlton Cole scored what was the 50th Premier League goal of his career.
Also in good scoring form is the home side's Kevin Nolan, who took his goals tally to six in his last seven appearances.
Southampton defender Maya Yoshida has scored two goals this season, both of which have come in away losses.
Crystal Palace 0-2 Manchester United
Departing Man United captain Nemanja Vidic, who will leave the club in the summer, made his 200th Premier League start for the Red Devils.
The encounter at Selhurst Park also marked David Moyes's 40th match as Man United manager.
As for Palace, they have never beaten the Red Devils during the Premier League era and neither has their boss Tony Pulis.
Liverpool 4-3 Swansea City
Daniel Sturridge has now scored in eight successive Premier League matches, which has drawn him level with record-holder Ruud van Nistelrooy, who achieved the feat on two occasions.
The England international's brace of goals took his tally for the season to 18 in 19 matches.
Swansea's Wilfried Bony also scored twice, which were his first Premier League goals in England. He had only previously found the net at Swansea's Liberty Stadium.
Newcastle United 1-0 Aston Villa
After seven hours and 30 minutes of waiting, Loic Remy finally ended Newcastle's run without a goal.
The Queens Park Rangers loanee has now scored 12 times for the Magpies, making him the club's leading goalscorer.
As for Paul Lambert's Villa, they have now gone three matches without scoring a goal.
Norwich City 1-0 Tottenham Hotspur
The only goal of the game, scored by Robert Snodgrass in the 47th minute, came with the game's first shot on target.
The Scotland international's intervention also helped Norwich to beat Spurs for the first time in seven attempts.
Staying with Tottenham, their manager Tim Sherwood was beaten in the Premier League for only the second time since he took charge in December.
