Neither side could find a breakthrough at the Amex, but a stalemate will certainly have suited Albion more than the Toffees, who are slipping behind in the race for the top four.
For their part though, the Seagulls are now seven points clear of the drop zone with seven games left to play.
We’ve taken a closer look at that clash and the rest of this weekend’s Premier League action...
Fulham 0-1 Wolves – Visitors huff and puff to blow Cottage down
It was a huge opportunity squandered for Fulham on Friday night as they slumped to a late defeat against Wolves.
The visitors arrived at Craven Cottage in a funk of their own, and Scott Parker’s men should have gone into this one all guns blazing in an attempt to drag Newcastle United into that bottom three ahead of the rest of the weekend’s action.
Instead, Fulham wilted under the pressure, and succumbed to a last gasp strike from Adama Traore.
The Cottagers have taken just 10 points at home in the Premier League this season – the worst record in the division – and if they do go down, the inquest won’t take too long as to where they came unstuck this term.
Manchester City 1-2 Leeds United – Dallas serves up soap opera drama
Saturday’s stoppage time win at the Etihad will surely go down as one of the fondest memories that Leeds United will have from a season that has already delivered so many.
Reduced to 10 men before half-time, it would have been a gargantuan task in itself if the Whites had managed to keep this one from becoming a cricket score against Pep Guardiola’s rampant champions elect.
Instead, Leeds defended valiantly, and when Stuart Dallas broke away in the dying seconds to slot home his second of the match, you could practically hear the roar from the other side of the Pennines.
Liverpool 2-1 Aston Villa – VAR, VAR, VAR
Like a spoilt brat trying to blow out the candles on another child’s birthday cake, VAR continues to insist upon making itself the centre of attention – and ruining the party in the process.
At Anfield this weekend, it was a marginal offside that caused controversy and confusion as Roberto Firmino had an opening goal ruled out, and were it not for a stoppage time winner from Trent Alexander-Arnold, the decision could have cost the Reds two valuable points.
It’s a point that’s been made a thousand times already, but there has to be some kind of review into how video technology is being implemented in the Premier League.
Crystal Palace 1-4 Chelsea – Blues bounce back
At the risk of sounding like one of those inspirational quotes you see bandied around on Facebook, it’s not necessarily about the falls you take, but about how you pick yourself up after them.
That was absolutely the case for Chelsea this weekend, who responded to being thoroughly Allardyced at Stamford Bridge last Saturday by lashing Crystal Palace seven days later.
Three goals up inside half an hour, it’s clear that Thomas Tuchel is dead set on securing a Champions League spot this term.
Burnley 1-2 Newcastle United – Saint-Maximin brings touch of divinity
There are plenty of hugely justifiable reasons for Newcastle United fans to be frustrated with their club, and Steve Bruce’s management in particular, this season.
But there are also some caveats to the relegation tussle that the Toon Army find themselves in, and it’s hard not to wonder where they might be in the table if they’d been able to rely on Allan Saint-Maximin’s ice cold genius on a weekly basis.
His match winning turn against Burnley – including an assist and a goal within nine minutes of coming on – was just his 18th Premier League outing of the campaign, and provided a stunning reminder of the impetus and invention he adds to the Magpies’ lineup whenever he is involved.
As for Burnley, Sean Dyche will be massively disappointed that his side threw away a lead against a side in the bottom half of the table for a second week running.
West Ham 3-2 Leicester City – Unplayable Lingard must play… or at least be in the squad
If four months ago you’d have suggested that Jesse Lingard should be in Gareth Southgate’s England squad for this summer’s European Championship, you would have been soundly, and fairly, ridiculed.
Fast forward to this weekend, and JLingz is the one having the last laugh.
Eight goals and four assists in nine Premier League matches since joining West Ham have turned the midfielder into the hottest form player in the Premier League, and it’s hard to look past him for a spot on that much-fabled figurative plane come June.
From a Hammers’ perspective too, those impossible Champions League dreams are inching ever closer.
Tottenham 1-3 Manchester United – Jose on the rocks
To anyone with even a passing interest in the Premier League, Jose Mourinho’s current plight at Tottenham is becoming eerily familiar.
After a bright start and plenty of catchy soundbites to woo the fanbase and the media alike, the mood in north London has soured like week-old milk, and the disgruntled barbs have begun to fly with increasing frequency and venom.
No matter which way you cut it and whatever excuses you cook up, however, Spurs are six points adrift of the top four with seven games left to play.
The issue with implementing a siege mentality everywhere you go is that sometimes those inside the keep are liable to starve.
Sheffield United 0-3 Arsenal – Blades bowing out with a whimper
Nobody in their right mind would have expected Paul Heckingbottom to keep Sheffield United up after they parted company with Chris Wilder earlier in the year.
At the very least, however, supporters would have been justified in asking for a little bit of fighting spirit from their team.
We saw glimpses of it against Leeds last weekend, but this time around against Arsenal it was back to square one as the Blades put in a typically lacklustre display.
It’s time to start focusing on next season, because this campaign has been a washout.
West Brom 3-0 Southampton – Big Sam finds his mojo
Last weekend’s stunning win over Chelsea at Stamford Bridge would have mattered for little if West Brom couldn’t back it up with a victory against Southampton on Monday night.
Of course, the Baggies did just that – and how, by the way – and what was looking like an impossible great escape now appears ever so slightly less daunting.
Albion are still six points adrift with seven to go, but they’ve got a wind their sails.
This might not be over just yet.
Brighton 0-0 Everton – Albion inching closer to safety
Brighton really look to have turned a corner in recent weeks.
Finally, after showing promise for months and months, they are starting to grind out the results they need to eke their way to safety.
Monday night’s stalemate against the Toffees was no classic, but at this stage of the season, entertainment value has to play second fiddle to pragmatism.