Brighton have been battling relegation all season but pulled away with goals from Leandro Trossard, Danny Welbeck and Neal Maupay.
“I’m really pleased, I thought the performance was fantastic,” Brighton boss Graham Potter said. “From the start we were brave, smart, worked hard and then reacted when we lost the ball.
“Newcastle hit the post early in the second half and like every Premier League game you have to survive those moments but I thought we were the dominant team. We thoroughly deserved to win.
“I am really pleased for the guys. They have been working hard and when you score it makes the game a lot easier.”
While it’s a boost for the Seagulls, it leaves Newcastle deep in a relegation battle after six games without a win, sitting two points above Fulham in 18th.
Newcastle boss Steve Bruce said: “It’s difficult to digest at the moment. We were nowhere near good enough on the night. Brighton were better in every department.
“We had to be good without the ball. We had to do far more ourselves with the ball. It was a painful one.”
He continued: “I take the full responsibility for it. We’ve worked tirelessly all week and unfortunately it unraveled very very quickly.”
On Friday night, Fulham were unable to make ground after a 2-1 home loss to Leeds United, with Patrick Bamford and Raphinha scoring for the Whites.