By the time Jan Bednarek, who scored an own goal in the first half, was sent off for a brushing against an already falling Anthony Martial in the 86th minute, Southampton were trailing 6-0 and hanging on grimly to avoid more humiliation.
Bruno Fernandes converted the penalty, and further goals by Martial and Dan James meant Southampton revisited a score they thought they would never see again.
"What can I say? It is horrible," Hasenhuttl said.
By being relentless in their search for goals, United's goal difference soared to +19, just five behind first-place Manchester City. That is all that's separating the two local rivals, who both have 44 points.
In 2012, City won the Premier League for the first time courtesy of a superior goal difference to United.
"You never know what might be the deciding factor," said United manager Ole Gunnar Solskjaer. "We know better than anyone what goal difference can do to you."
Remarkably, Southampton weren't the only team to finish with nine men, with Arsenal also having two players sent off — defender David Luiz and goalkeeper Bernd Leno — in a 2-1 loss at Wolverhampton. The result ended Arsenal's seven-match unbeaten run in the league.
After going the first 17 games without a win Sheffield United have now won three of their last five after rallying to beat West Bromwich Albion 2-1 at home. Palace beat Newcastle 2-1, with Gary Cahill grabbing the winner to become — at 35 years and 45 days — the club's oldest scorer in the Premier League.
- AP