Manchester United midfielder Jesse Lingard made the difference for Brighton on debut.
He earned the match-winning penalty on his debut for new loan club Brighton & Hove Albion.
The winger, who scored for United's Under-21s six days ago, was fouled in the area by Millwall defender Danny Shittu and Diego Lopez converted the resulting spot-kick. Lingard was reunited with his former Reds team-mate Tomasz Kusczak, who kept a clean sheet as Brighton held on for a hard-fought 1-0 away win.
