Manchester City went temporarily top in the Premier League following a hard-fought 1-0 away win against Bournemouth on Saturday.
The hero for City was substitute Riyad Mahrez, who after replacing the injured Kevin De Bruyne, scored in the 55th minute.
The win took City to 71 points, just two points above Liverpool who, on 69 points, will face Everton at Goodison Park on Sunday.
At Old Trafford, Manchester United gave their top four pursuit a big boost with a 3-2 win against relegation threatened Southampton.
Southampton opened scoring in the 26th minute through Yan Valery whose 25-yard strike put his side 1-0 up.
United suffered another injury setback as Alexis Sanchez went off with a knee problem in the 52nd minute and was replaced by Diogo Dalot.
In the 53rd minute, Andreas Pereira equalised to make it 1-1 for the Red Devils off a superb long range shot.
Just six minutes after Pereira’s equaliser, Romelu Lukaku made it 2-1 in favour of United.
Southampton drew level on 75 minutes of thanks to James Ward-Prowse with a brilliant freekick.
But in the 89th minute, Lukaku scored what proved to be the winner to give United a 3-2 lead.
United were awarded a penalty in the 94th minute only for Paul Pogba’s effort to be saved.
United replace Arsenal in fourth place on 58 points while Southampton are 17th on 27 points, two points above the drop zone.
In other results, Crystal Palace beat Burnley 3-1 away, Wolverhampton Wanderers defeated visiting Cardiff City 2-0 and Brighton and Hove Albion secured their first three points of 2019 with a 1-0 win against bottom club Huddersfield Town.
Man United 3-2 Southampton
Bournemouth 0-1 Man City
Wolves 2-0 Cardiff City
Burnley 1-3 Crystal Palace
Brighton 1-0 Huddersfield Town