Both teams are on 44 points although United have played two more games with City travelling to Burnley tomorrow.
Southampton, already weakened by injuries, were reduced to 10 men after 79 seconds and lost another four minutes from time and drop to 12th on the table.
Newcastle United came back to earth with a bump as Crystal Palace recovered from conceding an early goal to claim a 2-1 victory at St James' Park.
Buoyed by their weekend win at high-flying Everton to snap a run of five successive league defeats, Newcastle loss left them in 16th spot, eight ahead of third-from-bottom Fulham who have played two games fewer.
Palace are 13th.
Arsenal finished with nine men as they slumped to a 2-1 defeat at Wolverhampton Wanderers, who ended an eight-game run without a win in the Premier League.
Arsenal dominated the first half, but lost David Luiz just before the break, with Wolves converting the subsequent penalty.
Goalkeeper Bernd Leno was red-carded in the 72nd minute for handling the ball outside his area.
The Gunners stay 10th with Wolves 13th.
Bottom side Sheffield United gave their survival hopes a shot in the arm with a third victory in five games after coming from behind to beat fellow relegation candidates West Bromwich Albion 2-1.
Victory moved Sheffield to 11 points from 22 games, 10 points away the safety zone and one behind 19th-placed West Brom.