Garth Crooks' team of the week: Sanchez, Kante, Luiz, Cech
Chelsea were held to a 1-1 draw at Burnley but still moved 10 points clear at the top of the Premier League, while Liverpool climbed to fourth after beating second-placed Tottenham 2-0.
Arsenal moved from fourth to third after a 2-0 win over Hull City, with Manchester City, who play at Bournemouth on Monday, dropping from from third to fifth.
Elsewhere, there were wins for Swansea against Leicester, Manchester United at home to Watford, Stoke against Crystal Palace and Southampton at Sunderland. The games between Middlesbrough and Everton, and West Ham against West Brom ended in draws.
Do you agree with my team of the week or would you go for a different team? Why not pick your very own team of the week from the shortlist selected by BBC Sport journalists and share it with your friends?
Goalkeeper - Petr Cech (Arsenal)
Cech's save from Oumar Niasse at 0-0 was crucial, bearing in mind the reputation of Arsenal manager Arsene Wenger is at stake. Another save by Cech from the same player in the second half was just as important and for the same reason. In these circumstances, when fans are exerting pressure on the manager, it's vital that players respond in a manner that alleviates that pressure.
Cech and Alexis Sanchez have the ability to do that, but what about the rest? Precisely what Kieran Gibbs was doing impeding Lazar Markovic when he was the last line of defence I don't know - it could have spelt disaster for Wenger. Down to 10 men at that stage of the game? If ever there was a moment when the entire match could have blown up in Wenger's face then that was it.
Cech displayed (and Sanchez for that matter) that not only can he cope with real pressure but he can be relied upon not to freeze at critical moments. A valuable asset to have in a crisis.
Defender - Eric Bailly (Manchester United)
Those of you who partake in social media (I don't) might know I was on a train from Manchester to London and spent longer than normal (because of a delay) talking to a number of Manchester United fans. They seemed reasonably satisfied with the win against a very dangerous Watford and after a little more probing they suggested that Eric Bailly might be a candidate for my team of the week.
Taken aback by this level of impertinence and their intrusion into my team of the week, I thought I would make further enquiries about Bailly's performance to see if they had a case! I must say I don't normally take fans' comments seriously - but in this instance they were spot on.
My problem with Bailly is he goes into tackles at such speed he leaves no margin for error and always appears to run the risk of being cautioned or dismissed. That said, the boys I spoke to on the train were right - Bailly was composed on the ball and measured in the tackle against Watford. It's always a pleasure talking to genuine football fans who actually know their stuff.
Defender - David Luiz (Chelsea)
This was by no means a straightforward fixture for league leaders Chelsea but a massive point nevertheless. If the Blues were not on top of their game this was a match they could have easily lost. As it happens, Burnley were restricted to one chance largely because of the positioning expertise of David Luiz, who only made one mistake in the match.
Remember, Luiz is playing Premier League football, and has done for about three weeks, with a heavily strapped knee. The Brazilian is doing manager Antonio Conte an enormous service by remaining part of the set-up but not without some obvious discomfort in order to keep the back five intact.
Conte has grown to trust Luiz in the way Mourinho used to trust John Terry. Teams cannot win titles without players making sacrifices or, to put it bluntly, play with injuries. Luiz's performance against Burnley, under the circumstances, was immense.
Defender - Alfie Mawson (Swansea City)
What a volley! I must say that had it been a centre-forward who had scored such an immaculate goal I couldn't have given the striker higher praise. The reality is that Alfie Mawson is a centre-back and I can't remember seeing a defender finish quite like that.
What Paul Clement is doing at Swansea is quite remarkable. Their victory over Leicester was his third Premier League win in four games and underpins his January manager of the month award.
As for Leicester, I have said it before and I will say it again - that the spectre of the Champions League is providing a false sense of security. Manager Claudio Ranieri has woefully failed to get his priorities right, lived off the kudos of relative Champions League success and all at the expense of their Premier League survival. It's a dereliction of duty and he will pay the price.
Midfielder - Martin Olsson (Swansea City)
I don't like playing players out of position but sometimes the occasion calls for it. Martin Olsson's performance against Leicester is one of those occasions. I watched Olsson play at Norwich under Chris Hughton and liked his performances. He seemed more than comfortable in the Premier League so I am not the least bit surprised he has returned to the top tier with Swansea.
He is clearly very comfortable on the ball and calm in front of goal. He absolutely hammered his shot past Kasper Schmeichel to put Swansea 2-0 up and condemn Leicester to a relegation dogfight for the rest of the season. The look on Claudio Ranieri's face at full-time said it all. He may have blown this.
Midfielder - N'Golo Kante (Chelsea)
It was N'Golo Kante - also known as 'the silent force' - who gave Eden Hazard the first clear chance of the game against Burnley and also the man who started the counter attack that resulted in Pedro's opener for Chelsea. Basically, Kante continues to provide the Blues with the steel required to repel any threat to their title challenge.
For periods in the second half Burnley became that challenge - and it took all of Kante's ingenious play to keep the Clarets at bay.
As a consequence, Chelsea gained a point they might have otherwise lost and in doing so retained the momentum and increased their lead at the top of the table.
Midfielder - Juan Mata (Manchester United)
This gentleman is one of the most professional players I have ever had the pleasure to meet. I interviewed him when he was a Chelsea player before he was shown the door by Jose Mourinho and sold to Manchester United - only for the man who flogged him to United to follow him to Old Trafford.
You think at this point it's only a matter of time before Mourinho moves Mata on once more. Not only does Mourinho mess the Spaniard about with tactical substitutions that only he understands - and at moments in the game that seem insignificant - Mata always seems to rise above it.
It has got to the stage where not only has Mata displayed remarkable professionalism, he is now playing as well for United as he did when Mourinho decided to sell him at Chelsea - which rather suggests to me that he has become saleable again and therefore may be the first in Mourinho's cull come the end of the season. Watch this space.
Midfielder - Ryan Bertrand (Southampton)
This lad has lovely quality on the ball. A defender's first priority is to defend but it makes all the difference if he can deliver quality balls into the box for strikers to attack and defenders to fear. Ryan Bertrand set up Southampton's first goal and created the third, all because he has quality on the ball and therefore is not afraid to put his ability on the line, by getting in positions that will expose him if he hasn't got what it takes.
Bertrand has come a long way since his days at Chelsea dreaming of being the next Ashley Cole. By leaving Stamford Bridge for Southampton, the England international has done something far more rewarding than that - he's actually found himself, which is far more worthwhile than trying to be someone else.
Forward - Sadio Mane (Liverpool)
I don't know what it is about Spurs and Anfield but they have only won there eight times in 81 league visits. What's that about? The person responsible on this occasion for continuing Tottenham's dismal record against Liverpool was Sadio Mane.
The Senegal international, fresh from the Africa Cup of Nations, could have scored four goals and should have scored a hat-trick in six minutes. Suddenly, the team with one of the best defensive records in the league looked like a unit that had never played together before.
However, it was the honesty of Mauricio Pochettino that made me think that Spurs still have the desire to finish in the top two. "We started only four points above Liverpool, but we didn't look like that today," said the more than slightly irritated Argentine.
Spurs fans can forget league titles if their team can't go to Anfield and get a result… Chelsea did.
Forward - Manolo Gabbiadini (Southampton)
Boy, do I like this striker. His goal last week against West Ham made me sit up and take notice but his two against a battered Sunderland were moments of predatory genius. Make no mistake, if Gabbiadini doesn't get a touch on the ball that comes off Lamine Kone's head the ball doesn't enter the net.
However, his second goal was sensational and reminiscent of his Italian countryman Filippo Inzaghi at his best. There is so much about Gabbiadini's game that reminds me of Inzaghi - not least his finishing.
Meanwhile, there is something very troubling about Sunderland's inability to capture the momentum they created after their victory over Crystal Palace last week. The Black Cats looked like they were caught in the headlights waiting for the inevitable to happen - and it did of course. The bench looked more disillusioned than the team.
Forward - Alexis Sanchez (Arsenal)
Is Alexis Sanchez keeping Arsene Wenger in a job? If Arsenal had lost to Hull at home, (in light of recent results) and they could have if not for Petr Cech in goal and Sanchez up front, the calls for Wenger's departure might have become unbearable.
Sanchez and Cech are the only two consistent performers in a team full of ability and short on bottle. I've already sung Cech's praises but Sanchez seems like the only outfield player at Arsenal that actually appears to want to win something and not just settle for fourth spot.
The Champions League comes into view this week and I'm not entirely sure if that's a help or a hindrance for the Gunners. What is clear is that Arsenal need to keep Sanchez whatever happens. Anything that can be done to achieve that will probably save Wenger from any further criticism.