The best chances came in the second half, with Newcastle almost finding an opening three minutes after the break.
Isaac Hayden hit a low shot that took a deflection and Mathew Ryan did well to save low to his right. The resulting corner found Jamaal Lascelles but he could only head wide of the post.
Newcastle also went close on 57 minutes after Dwight Gayle got between two Brighton defenders and put his header goalwards, but Ryan was on hand, diving to his left to save and keep the scores level.
The visitors got into the action on 68 minutes when Shane Duffy headed a corner back across goal that was met by the forehead of Lewis Dunk, however this time it was the Newcastle goalkeeper who made the good stop as Karl Darlow palmed it away.
Both teams did have a couple of opportunities in the first half to find the back of the net, including on 21 minutes when Gayle did well to reach a ball and then pull it back towards goal. Ryan could only parry it but, luckily for the goalkeeper and the Seagulls, the parried ball was just out of reach of the incoming Joselu inside the six yard box.
Duffy nearly sent the visitors into the break ahead but his header three minutes before half-time just floated over the bar.