United survived Southampton's second-half onslaught to hold out for a crucial away win and keep pace with the Premier League leaders.
The Reds dominated the first 45 minutes and went ahead through Romelu Lukaku's eighth of the season and it was a goal that we were left clinging on to in a backs-to-the wall rearguard.
Saints pinned United deep in their own half after the break but - for all their possession and territory - David de Gea remained relatively untested.
United manager Jose Mourinho was sent to the stands by referee Craig Pawson as tensions boiled over during the frenetic final moments. The result means that United have lost ground on City in terms of goal difference, but we remain level on points with Pep Guardiola's men, with Chelsea two points further back.
Henrikh Mkhitaryan fired wide early on before United went in front in the 20th minute.
Ashley Young's cross picked out Lukaku and, after Fraser Forster had parried his initial header, the Belgian snaffled up the rebound from close range.
Marcus Rashford went close with a free-kick soon afterwards, before Mkhitaryan fired wide after he had burst into the box with a mazy run. That proved to be the final action of the half, and Saints soon found themselves on the front foot as United came under heavy pressure.
Oriol Romeu flashed an effort fractionally wide on the turn, de Gea denied Nathan Redmond from distance and Eric Bailly cleared well under the attention of Shane Long.
United substitute Ander Herrera fired over and Forster denied Lukaku with his foot before Steven Davis went close with a 25-yarder at the other end.
Marouane Fellaini headed off the line to keep out the increasingly influential Romeu, who had a superb game alongside the also impressive Mario Lemina in the heart of the Saints midfield.
Saints introduced the fresh legs of Manolo Gabbiadini - who scored twice against us in the EFL Cup final - and he was quickly involved in his side's push for a leveller.
He exchanged passes with Dusan Tadic, who in turn picked out Romeu, and his first time shot across goal flashed beyond the far post.
Southampton continued to press and forced a succession of corners in the dying minutes, but United's miserly defence stood strong and held out for a hugely important victory.
Jose was sent off in the final minute after he inadvertently strayed on to the pitch in an attempt to help the team run the clock down.
Overall team performance: 6.5/10
United Faithful Man of the Match: Phil Jones. Stayed strong and was great in the air under a late bombardment
NB: A special mention to the 3,500 travelling Reds who did the club proud with their magnificent vocal backing throughout on the longest away trip of the season