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- Ratings: Fred, Matic struggle in Man Utd draw at Southampton
United have equaled Arsenal's away streak during their unbeaten campaign during the 2003-04 season.
Paul Pogba provided another assist to rack up his fifth of the campaign already but United were unable to grab all three points.
Salisu was on hand to block Pogba's close range shot minutes later while the United midfielder also headed a good chance over the bar.
The hosts hung on and took the lead against the run of play after 30 minutes when Adams' strike from outside the box was deflected off found and found the bottom corner.
Southampton held on to the lead until the 55th minute when Pogba drove into the box to set up Greenwood to score the equaliser.
Pogba also came close to putting United in front moments later with a fine solo run but he flashed his shot just past the post.
Just after the hour mark, the visitors produced a swift counterattack which Greenwood unable to head home from Fred's cross.
Southampton almost capitalised on a Maguire error after 75 minutes when Adam Armstrong was put through but De Gea made a good save to deny him.
United battled to find a winner but Southampton defended well to record their first point of the league season.
Greenwood praised Southampton's performance but criticised his side for not capitalising on the equaliser.
"It was a difficult game, Southampton defended well but in my eyes we dropped two points," he told Sky Sports.
"When we got the equaliser we should have gone for the throats, the time went away and we did not get the winner towards the end."
Southampton right back Valentino Livramento said his side had chances to take all three points but he was happy with one.
"We knew the way we could compete was by being physical and aggressive with the press and hitting them on the counter," he said.
"I feel we could have won the game, maybe could have lost the game, but a draw is a fair result."