The visitors were forced to line up with Scott McTominay and Nemanja Matic in defence due to injuries and found themselves two goals down after only 20 minutes at St Mary's Stadium.
Romelu Lukaku got a goal back, his first in the Premier League since September, and Ander Herrera secured a point, but a top-four finish is beginning to look a tall order for Mourinho's men.
Hughes, who has been facing calls for the sack himself, has now failed to steer Saints to a win in eight consecutive games in all competitions.
United failed to capitalise on a missed kick from Alex McCarthy three minutes in, and they were punished when Stuart Armstrong blasted across David de Gea's goal and into the net with Saints' first effort on target.
St Mary's was bouncing seven minutes later when Cedric Soares bent an unstoppable free-kick into the top-left corner from 25 yards out, after Marcus Rashford had lost possession and brought down Mario Lemina.
Rashford's poor opening half-hour was summed up by a wayward strike over the bar, but the England forward made amends when he shouldered Maya Yoshida off the ball and played in Lukaku to smash home 12 minutes before the interval.
981 - Romelu Lukaku's strike vs Southampton has ended a run of 12 games and 981 minutes without a goal for Manchester United in all competitions since netting against Watford in September. Relief. pic.twitter.com/xpoVjUoa1X— OptaJoe (@OptaJoe) December 1, 2018
And it was Rashford's brilliance that set up Herrera to make it 2-2 before the break, the 21-year-old bursting through the Saints defence and cutting the ball back for his team-mate to backheel into the net.
United, who lost former Saint Luke Shaw to a knock midway through the second half, dominated much of the play but struggled to threaten McCarthy's goal, and David de Gea had to make a strong save to stop Nathan Redmond's stinging strike from snatching victory.
What does it mean? United show character but top four is slipping away
United will be happy to leave with a point given the ineptitude they displayed in the first half-hour, but it is now three games without a win in the Premier League for Mourinho's men.
The result means Manchester City are 16 points ahead of their rivals at the top of the table, while United could be nine adrift of the top four if Chelsea beat Fulham on Sunday and Tottenham draw with Arsenal.
Southampton are up to 18th, but letting a two-goal lead slip might not be sufficient to spare Mark Hughes the sack if wins do not follow soon.
Rashford shows powers of recovery
It was a difficult opening half-hour for Rashford, who missed a hatful of chances against Young Boys in his last outing, but the way he dragged his side back into the game with two excellent assists highlighted a commendable determination to impress his manager.
2 - Marcus Rashford has provided two assists in a single game in all comps for Man Utd for just the second time in his career (also vs Crystal Palace in September 2017). Catalyst. pic.twitter.com/Lkw4zMo0X6— OptaJoe (@OptaJoe) December 1, 2018
McTominay out of position and out of luck
McTominay was part of a back three out of necessity, with Chris Smalling and Eric Bailly having picked up pre-game injuries, and an uncertain display was underlined by some strange positioning behind the wall for Cedric's strike.
United head into back-to-back home games next week, starting with the visit of Arsenal on Wednesday before Fulham travel to Old Trafford on Saturday. Southampton visit Tottenham and then Cardiff City on those same dates.