The Foxes came from two goals down to draw 2-2 thanks to late goals from Jamie Vardy and Bobby De Cordova-Reid.
It's seen Leicester steer five points clear of the relegation zone and ensure Van Nistelrooy remains unbeaten as their manager.
He has won four points from two Premier League matches, a tally that sees him equal Manchester United's new head coach.
Amorim has taken charge of three league fixtures since he replaced Erik ten Hag as his permenent successor last month.
The Portuguese drew 1-1 with Ipswich Town on his first outing and then beat Everton 4-0 on his second.
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However, United's 3-2 defeat at home to Nottingham Forest means Amorim has won only four points from a possible nine.
Van Nistelrooy, who was the United interim head coach prior to Amorim's arrival, has therefore match his points in one less game.
He first beat West Ham 3-1 on Tuesday night, which was the club's first league win since October.
The Dutchman was then able to grasp a crucial point against Brighton as the Foxes netted goals in the closing moments.
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Tariq Lamptey opened the scoring with an excellent curling effort from the edge of the area when heading towards half-time.
Yankuba Minteh then netted what looked to be the winner for the Seagulls with a low finish after some neat skill on 79 minutes.
However, Vardy slotted in shortly after before assisting De Cordova-Reid in the opening minute of stoppage-time to make it 2-2.
Leicester have risen to 16th in the table following the draw and above Crystal Palace with 15 games played.
Van Nistelrooy will hope his side's late heroics will provide confidence ahead of a testing run of fixtures.
After matches against Newcastle and Wolves, Leicester face leaders Liverpool before Manchester City and Aston Villa.