Ole Gunnar Solskjaer’s men were unable to take advantage of weekend defeats for Chelsea and Leicester to remain in fifth.
United had become the first side in Premier League history to win four consecutive games by a three-goal margin, but there was no cruise for the Red Devils this time even after they responded to Stuart Armstrong’s early opener.
Two goals in as many minutes from Marcus Rashford and Anthony Martial turned the game around, but United were caught out by a corner deep into stoppage time when substitute Obafemi turned home Jan Bednarek’s flick on.
Manchester City’s victory over UEFA in the Court of Arbitration for Sport earlier on Monday upped the pressure on United to continue their impressive form with only a place in the top four now good enough for Champions League qualification.
Solskjaer will still be confident of achieving that goal as his side have closed an eight-point gap on Leicester, who they face on the final day of the season, since the Premier League’s restart.
But two dropped points were a reminder that United are far from the finished article if they aspire to challenge Liverpool and Manchester City for the title next season.
A 17-match unbeaten run looked in danger early as Southampton — who have been in impressive form themselves since the Premier League’s return last month — were rewarded for a bright start at Old Trafford.
Paul Pogba’s return from injury has played a big part in United’s free-scoring run, but the Frenchman was at fault for the opening goal as he was caught in possession by Danny Ings.
Redmond then crossed for the unmarked Armstrong at the back post and the Scottish international took a touch before flashing a shot past De Gea.
– Firepower –
United have now scored 16 goals in their last five league games to close the gap on Chelsea and Leicester in the top four race.
That firepower was in evidence as the game was turned on its head within two minutes as Martial showed great strength and touch to tee up Rashford to slot home his 21st goal of the season.
Both Rashford and Martial are enjoying their best ever scoring seasons and moments later it was the Frenchman’s turn to score his 21st of the campaign as he powered past Kyle Walker-Peters before lashing a shot past Alex McCarthy for his 50th Premier League goal.
Southampton were lucky to get into half-time with just 11 men on the field as Oriol Romeu somehow escaped sanction despite a VAR review for a dangerous lunge on Mason Greenwood.
The Saints stemmed United’s flow at the start of the second half and Solskjaer responded by replacing Pogba with Fred.
Rashford and Martial still had chances to kill the game as Ryan Bertrand’s block denied the English international a certain second before Martial slashed a shot wide after a purposeful run from the halfway line.
United were given a warning five minutes from time when De Gea produced a stunning save to turn Redmond’s effort over to bounce back from a couple of errors leading to goals since the Premier League’s restart.
The hosts were left down to 10 men for the final few minutes as Brandon Williams was taken off with a head injury after Solskjaer had used his allocated three stoppages to make substitutions.
And they were caught out as Obafemi was in the right place to claim a point for Southampton.