Early goals from Ryan Fraser and Fabian Schar saw The Magpies go 2-0 up inside the opening quarter-hour.
Brighton pulled a goal back in the second half as Lewis Dunk turned the ball in from a corner to reduce the deficit but Newcastle were able to hang on.
Our writer Dominic Scurr has dished out his player ratings from the the match…
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1. Martin Dubravka - 6
Made a smart save to deny Danny Welbeck in the first half. Should have done better for Dunk's goal but made a good stop at his near post to deny Trossard in the closing stages. Photo: Shaun Botterill
2. Emil Krafth - 7
Worked hard and got forward well. One of his better displays. Photo: Stu Forster
3. Fabian Schar - 8
A fine header put Newcastle 2-0 ahead early on. Solid at the back. Photo: Stu Forster
4. Dan Burn - 8
Made several important blocks and tackles during the match to help contain Brighton's pressure. Photo: George Wood