The point keeps United in fifth - level on points with Leicester City who have a superior goal difference in the race for the two remaining spots for European club football's most prestigious competition.
"It's the worst time to concede a goal but it happens in football," said United manager Ole Gunnar Solskjaer of Obafemi’s 96th-minute effort.
“You have to be strong and take it. We've won so many games that way ourselves but it's all part of the learning for this team."
United became the first side in the 28 years of the English Premier League to win four consecutive games by a three-goal margin as they closed in on a place in the top four.
And despite Marcus Rashford and Anthony Martial responding with two goals in as many minutes to overturn Stuart Armstrong's early opener for Southampton, United could not establish a comfortable cushion.
Setback
And the hosts paid the price when substitute Obafemi turned home Jan Bednarek's flick with only seconds remaining.
"We didn't deserve three points," conceded Solskjaer. "We never got the rhythm in our passing today, especially after 2-1."
Ralph Hassenhuttl's Southampton remain in 12th place following the draw. His side - who were flirting with relegation before the lockdown - have won three and drawn two of their six games since the Premier League restart to keep themselves well away from the drop zone.
"We are becoming more brave," said Hassenhuttl. "You can feel the guys really enjoy what they are doing."
