Liverpool returned to the top four with a 3-0 victory over Burnley in their penultimate game of the season, leaving them in pole position to seal the final Champions League qualification spot on the final day.
However, Leicester City are only behind the Reds on goal difference and so could pounce on any slip-up, despite Tuesday's 2-1 defeat to fellow top-four hopefuls Chelsea, who are only one point clear of Liverpool and Leicester in third.
West Ham United now know that they simply need to avoid defeat on the final day to seal a Europa League spot, after they came from behind to beat West Bromwich Albion and Tottenham Hotspur were beaten at home by Aston Villa.
Everton's 1-0 win over Wolverhampton Wanderers means that if they better Tottenham's result on the final day then they should nick seventh place, and with it a spot in the inaugural UEFA Conference League.
Here, Sports Mole selects its Premier League team of the week for gameweek 37.
Kiko Casilla and Jordan Pickford deserve mentions, but for the third week in a row, Liverpool's Alisson Becker gets the gloves in this week's team - and without the need for any goalscoring heroics this time.
The Brazilian made four saves to keep a dangerous Burnley attack at bay, and also dealt with numerous high balls into the box to take pressure off the two centre-backs in front of him.
One of those centre-backs was Nat Phillips, who produced arguably the standout performance of the entire gameweek with valuable contributions at both ends of the field.
The Liverpool man made clearance after clearance from Burnley's crosses into the box - most notably one off the line to save a certain goal - and also scored his first senior goal to put his side 2-0 up at Turf Moor.
Phillips is joined in this XI by Andrew Robertson at left-back too, completing a trio of Liverpool selections courtesy of his two assists against Burnley.
Trent Alexander-Arnold was also in contention for a spot on the opposite flank, as was Luke Ayling, but right-back goes to Jacob Murphy, who not only helped Newcastle to keep a clean sheet against Sheffield United, but also assisted the only goal of the game at the other end.
Phillips was not the only goalscoring centre-back this week, with Adam Webster, Dan Burn, Antonio Rudiger and Angelo Ogbonna all getting on the scoresheet, but the final spot in the back four goes to Leeds' Liam Cooper, who returned to the side and made five tackles to help keep a clean sheet against Southampton.
Fulham have at least ensured that they are not going down with a whimper, and in different circumstances a 1-1 draw away to Man United would be a high point of a season. Andre-Frank Zambo Anguissa was instrumental in that result, helping to patrol the midfield and largely keeping the likes of Bruno Fernandes quiet.
Alongside him, Tomas Soucek was spared the ignimony of an own goal despite glancing Matheus Pereira's corner past his own keeper, but regardless of that intervention he made up for it later with the equalising goal, setting the Hammers on course for an important win.
A 1-0 home win over the league's bottom side is not always a recipe for being the joint-most represented club in a team of the week, but that is the case for Newcastle here as they provide two of the three just behind the striker.
Allan Saint-Maximin ran the Sheffield United defence ragged at times, completing 15 dribbles during the match - the joint-most by any player in Europe's top five leagues this season, equalling Lionel Messi of all people.
It was Joe Willock who stole the headlines yet again, though, scoring for a sixth successive Premier League match and becoming the youngest player in Premier League history to achieve that particular feat.
Indeed, Willock has arguably outperformed every Arsenal player since his loan move from the Gunners, although Nicolas Pepe did impress against Crystal Palace with two goals to see off competition from Bertrand Traore, Steven Bergwijn, Andros Townsend and Phil Foden in the wide areas.
Patrick Bamford continues to enjoy a stirling campaign in Leeds' first season back in the Premier League, adding his 16th Premier League goal of the season against Southampton - the most by a player for a promoted club since 2014-15, when Charlie Austin scored 18 for Queens Park Rangers.
Ten of those have come away from home - the first player to do that for a promoted club since Andy Johnson for Crystal Palace in 2004-05 - and Bamford also earned praise for staying on his feet when he could have gone down to win a penalty.
Sports Mole's Premier League Team of the Week (4-2-3-1): Alisson; Murphy, Phillips, Cooper, Robertson; Anguissa, Soucek; Pepe, Willock, Saint-Maximin; Bamford