Casemiro’s second red card of the season gave Southampton the numerical advantage, but they could not capitalize on it despite going close on several occasions.
Even before Casemiro‘s early exit for a dangerous tackle on Carlos Alcaraz, David de Gea needed to make a brilliant reaction save to turn away Theo Walcott’s close-range header.
De Gea then produced a one-handed save after the break when Walcott found himself running clear of the home defence, while Aaron Wan-Bissaka cleared off the line when Scott McTominay turned a Kyle Walker-Peters cross towards his own goal.
Southampton’s James Ward-Prowse also saw his free-kick skim the top of the bar and Walker-Peters hit a post with an angled drive.
Manchester United had their own dangerous moments, with captain Bruno Fernandes’ goal-bound effort tipped on to the inside of a post by Gavin Bazunu.
Meanwhile, West Ham United drew 1-1 with Aston Villa, which saw David Moyes’ struggling side move out of the Premier League relegation places on goal difference.
Villa striker Ollie Watkins broke the deadlock with a 17th-minute header from left-back Alex Moreno’s sublime cross, but Said Benrahma equalized from the penalty spot nine minutes later.
Benrahma was the standout attacking threat on either side at London Stadium, but he saw a powerful strike from distance tipped over by Emiliano Martinez in the second half.
Super substitute Miguel Almiron scored the winner with 12 minutes left as the Magpies ended a run of three straight defeats in all competitions to leapfrog Liverpool into fifth on goal difference and move within four points of fourth-placed Tottenham, who have played two games more.