Warren Joyce's side scored through Jesse Lingard, Larnell Cole and Frederic Veseli but Jake Sinclair, brother of Manchester City's Scott, netted two headers and Calum Chambers snatched a draw with virtually the last kick of the game.
In front of the watching Ole Gunnar Solskjaer, the former Reserves boss and current Molde manager, Joshua King soon tricked his way into the box following a Ryan Tunnicliffe flick and laid the ball back for Lingard. The midfielder's shot deflected off Matt Young and past Artur Boruc for a rapid breakthrough.
After Bebe shot wide in his first appearance at this new level, Boruc had to keep the Saints in the game. The former Celtic keeper made a splendid stop to thwart Bebe following a lightning break started by Lingard and fuelled by Tunnicliffe's turbo-charged run.
King muscled his way past Jack Stephens but shot too closely to Boruc and the Pole pushed away a stinging drive by Lingard after a spell of dominant possession by United. At the other end, Pierluigi Gollini was not extended in the first half on his first start at this level.
The Italian comfortably fielded attempts by Sinclair and Ben Reeves while Reeves and Steve De Ridder smashed over the bar as the visitors ensured the lead was a slender one going into the interval. Indeed, the Saints dominated play in the second half - even if United mustered the occasional threat.
Captain Tom Thorpe volleyed at Boruc from a corner and Lingard floated a bold curling drive onto the top of the net after Bebe won possession with a tackle inside his own half. But there could