Goals by Marcus Rashford and Anthony Martial seemed to have ensured United’s place ahead of Chelsea and Leicester City, but Michael Obafemi‘s flick into the net in 96th minute gave the Saints the vital draw.
Stuart Armstrong had gave the visitors the surprise lead in the 12th minute before Rashford and Martial answered in a high-paced first half.
Martial’s top left corner strike, moments after Rashford’s neat finish in the 20th minute, gave the France international 50 goals in his Premier League career.
But Southampton shockingly hit back when Obafemi guided Jan’s Bednarek header off a corner attempt.
With three league matches left for all sides, United (59 points) remain behind Chelsea (60 points) and Leicester on goal difference. League champions Liverpool and runners-up Manchester City — who had their UEFA ban successfully appealed on Monday — have already qualified for the top European competition.