Saints should have gone ahead within five minutes when Eric Bailly was adjudged to have handled in the area, but United goalkeeper Sergio Romero saved Manolo Gabbiadini’s penalty.
Bailly’s sharp shot then forced Fraser Forster into a solid save, as the United defender created his side’s best chance of the first half.
Southampton forced Romero to make multiple saves after the break but were unable to get past the United keeper before Anthony Martial hit the post for the visitors.
Relive Romero’s goalkeeping masterclass against Southampton
With Jose Mourinho’s side guaranteed a sixth-place finish before kick-off and one eye firmly on next Wednesday’s Europa League final, it always looked like being a sedate affair on the south coast.
Southampton had slightly more to play for with another top-eight finish in their sights in Claude Puel’s first season in charge, and were marginally the brighter side.
But their terrible run in front of goal at St Mary’s continued – they have now gone 365 minutes without scoring at home.
Martial could have won it for the away side but his fizzing shot from 25 yards came back off the inside of the post.