Despite the Gunners' victory, Manchester City are just two wins away from an unprecedented fourth successive title.
Burnley's one-season stay in the top-flight is over, with Luton all but certain to join them in the Championship.
AFP Sport looks at three talking points from the weekend's action:
Arsenal make Man City work
Arsenal's 1-0 victory at Manchester United on Sunday will not live long in the memory, but the gritty Gunners got the job done in draining conditions, securing a hard-fought result that could prove crucial in the title race.
Leandro Trossard scored the only goal of a sleepy encounter played in baking heat until a late thunderstorm.
Despite failing to hit the same heights as their performances in recent weeks, Arsenal's strong backbone ensured they did not hand the title on a plate to Manchester City.
In stark contrast to the brittle Arsenal defences that have been common in their 20-year drought since last winning the league, Mikel Arteta's men have now kept six clean sheets in their last seven away league games.
With Arsenal one point ahead of Pep Guardiola's men and likely to get the better of Everton at home next weekend, City need to win their final two games against Tottenham and West Ham to secure a record fourth consecutive English title.
Chelsea's Pochettino has long-term view
Mauricio Pochettino insisted he could stay at Chelsea for the long term after back-tracking on his claim that it would not be the end of the world if he was sacked.
On Friday, Pochettino raised doubts over whether he would be at Stamford Bridge next season with an honest appraisal of his situation at the end of a turbulent first season in charge.
But 24 hours later the Argentine, who had hinted he could quit rather than wait to be potentially dismissed by chairman Todd Boehly, was in a more optimistic mood after Chelsea scored twice in the last 10 minutes to beat Nottingham Forest 3-2 at the City Ground.
"I never said I am not happy. It is a normal headline and sometimes too much honesty, talking. It is not a problem," he said.
"I had an honest conversation in the press conference. To clarify, if the owner is happy with my job we can continue. I am always a coach who is thinking long term."
With two games left, Seventh-placed Chelsea remain in the hunt for Europa League or Europa Conference League qualification.
Burnley down as Luton face harsh reality
Vincent Kompany vowed not to sulk after Burnley's relegation as the Clarets boss set his sights on a promotion-winning campaign next season.
Only victory at Tottenham on Saturday would have kept alive second-bottom Burnley's faint survival hopes but, although Jacob Bruun Larsen's opener gave them hope, Pedro Porro equalised before Micky van de Ven scored the winner in the closing stages.
"I said, no sulking, no moaning, get on with it and I have an exciting team to work with," said Kompany, who led Burnley to the Championship title last season.
"I can guarantee you one thing that tomorrow is day one of us being successful again. Tomorrow is day one of next season for me."
Luton striker Carlton Morris tried to put their impending relegation into perspective after Saturday's 3-1 defeat at West Ham all but confirmed their demise.
The third-bottom Hatters are three points and, crucially, 12 goals adrift of fourth-bottom Nottingham Forest and know their one-year stint in the Premier League is likely to come to an end next week.
"At the end of the game, going over to our fans and being stood there for 10 minutes, the lads giving out shirts, them clapping us - it does touch a nerve to be honest and it does put things into perspective because these people work all week to come and watch us," Morris said.
