United took the lead in the first half and earned an early lead. Bruno Fernandes picked out Marcus Rashford behind Southampton's defence and he then squared a low-driven cross for Jadon Sancho to hammer home at the back post.
United were in control in the first half and went into the break ahead but like they have in their last two games, they were pulled back by the opposition and lost their lead moments into the second half.
Mohamed Amine Elyounoussi picked out Che Adams beautifully who then finished with precision off the inside of the far post and into the back of the net.
Story of the game
Cristiano Ronaldo came into the game without a goal in five matches, his worst dry spell since 2010. He had a wonderful opportunity thanks to Jadon Sancho's vision who found him brilliantly. The Portuguese forward took it around Fraser Forster but barely connected with his strike and Romain Perraud blocked the shot.
United took the lead after a brilliant counterattack just after the 20-minute mark. It came through Fernandes' excellent ball over the top for Rashford to chase. He then squared the ball across the box and Sancho tapped home at the back post.
Saints' opportunities came down the right flank either through Armstrong or Kyle Walker-Peters. The young right-back exploited the space left open and drilled in a good cross but neither Che Adams nor Armando Broja gambled to get their foot on the end of it.
Minutes before half-time, De Gea was called into action as Armstrong's acrobatic effort was headed for the far right corner. It was a relatively comfortable save in the end but he did particularly well to hold onto it.
Everything was going oh so smoothly for United as they cruised into the half-time break 1-0 up.
But moments into the second half, they were once again pulled back. This time by Adams who neatly finished past De Gea after a splendid poked through ball from Elyounoussi.
From then on, the match started to really open up as both teams pushed for a winner. Southampton were happy to try and break quickly through Broja and Adams, and they got the better of Varane and Maguire a few times.
Ronaldo headed through the legs of Forster and the fans at Old Trafford believed he had given them the lead but the linesman's flag went up and his goal drought continued.
Rangnick then made changes and brought on Anthony Elanga for Scott McTominay to make up the most attacking side he has ever played. Ronaldo and Rashford the strikers, with Elanga and Sancho on the wings and Fernandes and Pogba in midfield.
Maguire then had a glorious header saved by Forster in injury time to hold onto the point.