The Seagulls dominated early on with Daniel Harding, Paul Reid and Hart all going close, while at the other end Mark Quigley fired over for Millwall.
There were few chances for either side after the break and the game looked likely to end up in stalemate.
But Hart popped up to hammer the ball home at the second attempt, before Millwall's Mark Phillips saw red in the dying moments for a second booking.
Millwall boss Dennis Wise on the recent sale of Scott Dobie to Nottingham Forest:
"We didn't want Scott to go but it was out of our hands. It was a board decision taken for financial reasons.
"It makes it very difficult and although we can now bring in two players on
loan that won't be easy to do as a lot of teams don't want to lose players at
"I was pleased with Quigley and Curtis Weston against Brighton and from now
on some of our youngsters will get opportunities."
Brighton: Shaaban, Reid, Hinshelwood, Butters, Harding, Hart, Carpenter, Nicolas, Knight, McCammon (Oatway 69), McPhee (Mayo 57).
Subs Not Used: Watson, Yelldell, El-Abd.
Goals: Hart 90.
Millwall: Marshall, Phillips, Lawrence, Ward, Craig, Weston (Serioux 82), Morris, Elliott, Sweeney (Trevor Robinson 62), Quigley (May 89), Dichio.
Subs Not Used: Simpson, Braniff.
Sent Off: Phillips (90).
Booked: Quigley, Elliott, Lawrence, Phillips.
Ref: A Marriner (W Midlands).