Albion were on the ropes in the first half and Southampton got their deserved lead when Broja finished well on the 29th minute after a poor clearance from Brighton keeper Robert Sanchez.
But once again Graham Potter's team displayed their fighting spirit and levelled in the dying moments as Maupay controlled and finished with a sublime volley after Jakub Moder's freekick.
It's the third time this season the French striker has earned Albion late 1-1 draws following his heroics at Crystal Palace earlier this season and also in midweek at West Ham.
Brighton were also down to 10-men at the end - as they were at West Ham - after a nasty injury to Leo Trossard, who was stretchered off.
Scroll down and click through to see who shone and who struggled at St Mary's Stadium