To add to their woes, the Reds' top scorer Romelu Lukaku was forced off injured on a stretcher after just 10 minutes following a nasty clash of heads with Wesley Hoedt.
Paul Pogba had the ball in the net as the game entered its closing stages, but was rightly denied by the offside flag to summarise a disappointing day.
United would've gone into the match confident of getting back on track before the turn of the new year on the back of a string of three disappointing results, having beaten the Saints at St. Mary's earlier on in the campaign.
However, the failure to defeat Mauricio Pellegrino's men meant the torrid record of not being able to defeat Southampton home and away in the same season since 2012-13 was to continue.
José Mourinho named three changes to the team that could only draw to Burnley on Tuesday. Victor Lindelöf took Marcos Rojo's place partnering Phil Jones in the heart of the defence – the Argentinian was replaced by Henrikh Mkhitaryan at the break earlier on in the week.
Jesse Lingard was also on at half-time as United trailed 2-0, stepping up and scored twice to make the final score 2-2, and both he and the Armenian started on the pitch for this one.
Mauricio Pellegrino made some surprising, yet expected alterations to the Southampton line-up, after their 5-2 thumping at Tottenham Hotspur last time out was the seventh match in their league winless run.
Fraser Forster has endured a poor season in goal for the Saints this season and dropped to the bench for Alex McCarthy, who was making his first Premier League appearance since March 2016.
Young defender Sam McQueen made his first Premier League start of the campaign alongside James Ward-Prowse and Dušan Tadić in place of Matt Targett, Mario Lemina and Nathan Redmond respectively.
Worrying Lukaku injury overshadows open start to proceedings
The start of the game was an open one, Southampton had come to play football, and the first real chance of the game fell to Romelu Lukaku after just four minutes.
Paul Pogba sprayed a delightful ball to Juan Mata on the byline before the Spaniard aimed his cross towards the head of the unmarked Lukaku, who could only head over the bar from six yards out.
It was then the visitors turn to go close three minutes later as dynamic winger Sofiane Boufal beat the offside trap near the byline to then cut the ball back into danger.
Luke Shaw's attempted clearance was calamitous and fell right in front of James Ward-Prowse, who hit a fizzing, low shot towards the bottom right corner, but David de Gea produced a fine diving save to deny him.
There was a major worry for Romelu Lukaku on nine minutes, after the Belgian striker clashed heads with opposing defender Wesley Hoedt and barely showed signs of movement on the ground.
Medics were quickly on the scene, delicately moving his head while placing him on a stretcher before carrying him down the tunnel - Marcus Rashford came on in his place three minutes after the collision.
Southampton were awarded a free-kick on the 20-minute mark, worryingly for United in the same position as where Burnley's first was produced earlier on in the week, after sloppy play by Victor Lindelöf.
The Swedish centre-back had at least five yards on Shane Long after the ball was played back, but instead of passing it back to de Gea he took a poor touch away from goal before fouling the rapid striker, who caught up to him in a flash.
james Ward-Prowse tried to catch the United goalkeeper out with the resulting free-kick from the left side of the pitch, but de Gea was alert and managed to beat the shot away for a corner at his near post.
United had the better of the first half chances
The visitors stayed at that end though, and nearly went ahead on 25 minutes, as Wesley Hoedt out-powered Nemanja Matić from a Ward-Prowse corner, but carelessly put his free header wide.
Despite Southampton growing in confidence, and into the game, it was the hosts who were pushing for an opening goal in the further stages of the first half.
Two chances arose around the half-hour mark. The first fell for Juan Mata after a big scramble in the away side's box resulted in the ball falling nicely for the no. 8 around 15 yards away from goal, but his shot was straight at Alex McCarthy, who forced the ball away with his feet.
Then a great, and common, piece of trickery by Ashley Young on the right flank made a bit of space on the byline for him to whip in a dangerous cross towards Marcus Rashford, but the young forward couldn't get over the ball and headed well wide.
The final opportunity of the half was wasted by Jesse Lingard after Henrikh Mkhitaryan got on the end of Paul Pogba's fantastic diagonal ball before exchanging a one-two with Mata.
A good cross into the area followed, but the side-on and unmarked Lingard directed a header wide of the post - he should've hit the target, but it wrapped up the tale of the first period for Manchester United.
Craig Pawson blew the half-time whistle which was met by a chorus of boos from the home crowd. The displeasure was either for Mr Pawson's seemingly okay performance, or for the Reds' inability to score before half-time at Old Trafford once again.
Resilient Saints hang on in uneventful second period
Southampton started the second half much brighter than Manchester United, and very nearly took the lead on 50 minutes when they caught the home side napping at the back.
James Ward-Prowse was given acres of space on the right and played a low ball across the pitch to Long in the centre. He hit a first-time strike towards the goal, but David de Gea was equal to it and pulled off a wonderful save with his feet to turn the ball over the bar.
Henrikh Mkhitaryan was brought off for Anthony Martial after 66 minutes, much to the pleasure of the Old Trafford faithful, who produced their loudest cheer of the evening for the switch.
Mkhitaryan is so low on confidence, and with the January transfer window looming around the corner, could that be the last we see of the Armenian midfielder in the famous red shirt?
In a hugely uneventful second half with the biggest talking points being the substitutes, we finally saw some action on minute 82 when Paul Pogba thought he'd given Manchester United the lead.
Ashley Young was brought down on the right wing before delivering the subsequent free-kick, the ball pinballed around the six-yard box as Nemanja Matić prodded it goalbound.
McCarthy saved the Serb's attempt, only for the ball the end up with Paul Pogba on the line and then into the net after the Frenchman poked it home.
The fans were jubilant, Pogba thought he'd bagged the decisive goal, but linesman Richard West played the role of Scrooge on celebrations by confidently raising his flag - the decision was correct.
Just three minutes were added onto the end of the match as United pushed for a winner, but the Saints defence remained resilient and held on for a hard-earned point on the road.
0-0 is a result the travelling Southampton fans definitely would've taken before the match got underway, even though it means the eighth consecutive match without a win is now part of their club's worst run in the top flight since a 10-game sequence from November 2004 to January 2005.
The two points dropped means that Manchester United now find themselves in third, a point behind Chelsea and unbelievably just three ahead of Liverpool after such a terrific start to the 2017-18 term.