Ander Herrera's goal — a deft flick at the near post — in the 39th minute earned United a point that will hardly be celebrated, as it still leaves Jose Mourinho's team six points off the Champions League qualifying places and a massive 16 behind first-place Manchester City.
Stuart Armstrong drilled in his third goal in two games to give Southampton the lead in the 13th, then Cedric Soares curled home a stunning free kick to put the team in sight of a first league win in three months.
United, however, managed to escape a fifth loss in its 14 league games, with Lukaku ending a 12-game drought in all competitions. Saints remained in the relegation zone and their winless top-flight run stretched to 10 games to keep the pressure on manager Mark Hughes.
With Chris Smalling joining Victor Lindelof and Eric Bailly on the injury list, United's resources at center back were stretched and center midfielders Scott McTominay and Nemanja Matic dropped into a three-man defense that was shaky early on.
Lukaku wasted a decent early opening, blasting straight at the onrushing Alex McCarthy after the Southampton goalkeeper swiped and missed with an attempted clearance. The hosts took that reprieve and sprung to life, with Armstrong driving home the opener after being teed up from Michael Obafemi, who was making his first start for the club. Rashford helped set up Saints' second, his scything challenge on Mario Lemina drawing both a yellow card and a free kick well in range of United's goal.
Cedric whipped his shot into the top corner. Rashford made amends by setting up two goals in six minutes. The England forward's throughball gave Lukaku the chance to hammer a finish high into the net in the 33rd.
Rashford then conjured another goal by getting to the byline and cutting back a cross that was slightly behind Herrera. The midfielder improvised by producing a fine backheeled finish.
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