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
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.