Meanwhile, the games at the St Mary's Stadium, Goodison Park and The Hawthorns ended in score draws.
Here, Sports Mole picks out the 11 players that made the biggest impression over the course of the weekend.
Petr Cech (Arsenal)
On paper Arsenal vs. Sunderland looked to be a home-banker, yet it was anything but that. The visiting Wearsiders provided some stern resistance and even had some decent chances, most of which were thwarted by the in-form Cech. His save to deny Steven Fletcher from close range when the score was locked at 1-1 was the highlight.
Erik Pieters (Stoke City)
Playing with a broken nose, Pieters took an eye-watering smack in the face against Man City. However, the Stoke left-back refused to let that unsettle him as he produced an exemplary performance. Kevin De Bruyne has shown some good form since joining Man City from Wolfsburg, but the Belgian playmaker was kept largely quiet by Pieters.
Winston Reid (West Ham United)
Man United produced what was arguably their best performance in recent weeks against West Ham, yet they still found goals impossible to come by. One of the major reasons behind that was the display of Reid, who made six crucial interceptions at Old Trafford. He also went very close to scoring, only to see his effort strike the post.
Fabricio Coloccini (Newcastle United)
For much of the season so far Newcastle's defending has been comical, but they somehow defied belief and the form book when a free-flowing Liverpool visited St James' Park. They kept an unexpected clean sheet, thanks largely to the impact of the frizzy-haired Coloccini, who made a number of important challenges and interceptions.
Adam Smith (Bournemouth)
There was no wonder goal from the right-back this week, yet his performance at Stamford Bridge was still a memorable one. Smith is a typical Eddie Howe-type player, in that he is neat and tidy in possession of the ball and also works hard for the team.
N'Golo Kante (Leicester City)
Any aspiring midfielders should get hold of a copy of Kante's performance at Swansea. It was pretty much a faultless display from the Paris-born player. He carried the ball with real purpose and also showed good vision in setting up his side's second goal. Not only that, he also made a host of interceptions, with no player having made more over the course of the season (64).
Aaron Ramsey (Arsenal)
Back fit and back in the centre of midfield, Arsenal's Wales international thrived. He made 124 passes, setting the tempo of the game in the process. It was his cross that saw Olivier Giroud make it 2-1 and then he made sure of the outcome with a goal of his own in stoppage time. It was his first goal of the season.
Riyad Mahrez (Leicester City)
After weeks of seeing Jamie Vardy hogging the headlines and limelight for Leicester, his Algerian teammate got in on the act at the Liberty Stadium. He was coolness personified in scoring an impressive hat-trick, becoming the first player from his country to have achieved that feat in the Premier League.
Xherdan Shaqiri (Stoke City)
With the greatest of respect, to look at, Shaqiri does not exactly scream athleticism. But, to his credit, he has a quick burst of speed and also has the vision and trickery in his weaponry to cause any defence problems. Man City found that out to their cost, with his two assists helping Stoke to record a deserved victory in the Potteries.
Bojan (Stoke City)
He may not have scored or assisted either of Stoke's goals in their impressive win over Man City, yet there is a case for suggesting that Bojan was his side's best player. The Spanish playmaker's first touch was impeccable throughout and more often than not it was he that started off the home team's attacks.
Marko Arnautovic (Stoke City)
His two fellow attacking teammates have been included, so there was no way that Arnautovic could be excluded. After all, the mercurial Austrian scored both of Stoke's goals, showing great predatory instincts in doing so. On another day he would have had a first-half hat-trick had his rising effort not struck the post.
Numpty of the week
Bastian Schweinsteiger: Man United's German midfielder can count himself ever so lucky that he escaped a red card during Saturday's clash against West Ham.
As the two teams prepared for a United free kick to be taken, the World Cup-winning captain drove his forearm into the throat of visiting defender Reid. It was a completely unnecessary act from someone so experienced and it could end up landing him a three-game suspension, having been subsequently charged with violent conduct by the Football Association.
Goal of the week
Marko Arnautovic - (Stoke City) vs. Man City: After he had broken the deadlock in the seventh minute, Arnautovic added an impressive second goal before the break.
In truth the finish was a relatively routine one, but there was nothing ordinary about the assist. Having spun away from Man City midfielder Fernando with a neat turn, Shaqiri then split the away team's defence with a precise pass that an advancing Arnautovic was able to guide beyond Joe Hart.