Stuart Dallas, Patrick Bamford, and Rodrigo scored the goals to give Marcelo Bielsa’s men all three points, and to keep them in the running for a top half finish.
As for Spurs, defeat severely dents their hopes of qualifying for the Champions League with three games left to play.
We’ve taken a look at that match, and the rest of this weekend’s Premier League action, below...
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Among various other soundbites and gripes, Steve Bruce has always maintained that it is only fair to judge his Newcastle United side when everybody is fit and available.
Detractors will justifiably argue that football doesn't work like that, and that sometimes you have to grind out results even when the deck is stacked against you, but it’s hard to deny that since they have welcomed the likes of Callum Wilson and Allan Saint-Maximin back to the side, the Magpies look like a force to be reckoned with.
There are still plenty of issues that need resolving up on Tyneside, but at the very least, another eye-catching performance against one of the Premier League’s top sides would suggest that there is plenty for the Toon Army to build on next term.
Leeds United 3-1 Tottenham Hotspur – Whites continue to bully the big boys
Arsenal, Chelsea, Liverpool, Manchester City, Manchester United, and now Tottenham – what do they all have in common?
Well, aside from trying to disembowel English football recently by attempting to form a European Super League, they also all have the distinction of failing to beat Leeds at Elland Road this season.
Marcelo Bielsa’s men were imperious on Saturday, and proved once again that they are more than capable of bloodying anybody’s nose on their day.
Looking ahead to next season, it’s hard not to be excited for a Leeds side that continues to blossom under the popular Argentine.
Sheffield United 0-2 Crystal Palace – Hard reset needed at Bramall Lane
Look, Sheffield United have been down for a long time – probably even before the maths confirmed it.
In that respect, it’s no real surprise to see them lose matches. After all, they’ve made a habit of underwhelming displays this term, and why would that change at such a late stage?
If there’s one thing that you could take from Saturday’s defeat to Crystal Palace, however, it’s that there needs to be a real rethink over the summer months.
This is a side devoid of confidence and quality, and if they head into next season with this kind of lukewarm showing, they might struggle in the Championship.
Manchester City 1-2 Chelsea – Tuchel wins psychological battle ahead of Champions League showdown
Few teams beat Manchester City once in a season, let alone twice in a month.
Thomas Tuchel deserves tremendous credit for the manner in which he has whipped this Chelsea side into shape since his arrival at Stamford Bridge, and once again he proved his tactical nous in a fascinating battle on Saturday evening.
With a Champions League final just around the corner, how rattled will this defeat leave Manchester City and Pep Guardiola?
Only they will know that, but Chelsea may just be favourites in a lot of people’s minds now.
Liverpool 2-0 Southampton – Reds still in with a shout
This time last year, nobody would have batted an eyelid at this scoreline.
Fast forward to the weekend, however, and it felt as if Liverpool’s victory over Southampton was a much-needed, and potentially vital, result.
Jurgen Klopp’s men are going to have to go hell for leather if they are to sneak into the top four, but a comfortable three points at home could just have the stabilising effect they need to give them a solid foundation going into their final four matches.
Wolves 2-1 Brighton – Albion undone by carelessness
If Brighton are to properly kick on next season, this is the kind of game that they have to be winning.
One goal up after 13 minutes against a very patchy Wolves side – the three points were there for the taking, and then some.
Instead, Lewis Dunk got himself dismissed, the Seagulls conceded two in the last quarter of an hour, and their afternoon was worsened even further when Neal Maupay was shown a red card at the final whistle.
In the grand scheme of things, this result doesn’t really matter, but it will sting Graham Potter nonetheless.
Aston Villa 1-3 Manchester United – The impossible dream is still alive
Manchester United could still win the Premier League this season.
They won’t, but technically they still could.
Man City's defeat to Chelsea couple with yet another comeback victory for Ole Gunnar Solskjaer’s men means that there is still a slim mathematical possibility that they could take the title back to Old Trafford, but the far more pressing – and impressive – takeaway from this game was the the Reds are slowly starting to look like a genuine elite-level side again.
West Ham 0-1 Everton – Hammers suffer blow
Three defeats in four have left West Ham’s hopes of an improbable Champions League qualification hanging by a thread.
The Hammers have outdone themselves all season, and David Moyes deserves massive credit for the job he has done at the London Stadium, but as old adage goes, it’s the hope that kills you, and to miss out on a seat at Europe’s top table after coming so close would be a galling blow for everybody associated with the club.
Arsenal 2-1 West Brom – The streak is over
Big Sam Allardyce – the greatest firefighter the Premier League has ever seen – has finally bitten off more than he can chew.
Defeat against Arsenal on Sunday consigned his West Brom side to the Championship after just one season back in the top flight, and it’s hard to argue that they didn’t deserve to go down.
All things considered, however, the Baggies have improved under the former England boss, and if they can keep hold of him this summer, they will have a very good chance of bouncing right back next term.
Fulham 0-2 Burnley – Cottagers down without a fight
For a while it really did look as if Fulham might pull off a great escape this season.
With a good wind in their sails and several Premier League rivals within touching distance, Scott Parker’s men were many people’s favourites to beat the drop, but they have floundered something awful in recent weeks, and nobody could have truly been surprised when Sean Dyche's men hammered the final nail into their coffin on Monday night.
As for the Clarets, they deserve credit again for the manner in which they have picked themselves up after a painfully slow start to the campaign.