The match pitched a five-game home losing streak against a four-game away losing run, but both were ended as neither side managed to break the deadlock.
The result sees the Magpies drop a place to 16th courtesy of Bournemouth's win over Everton, while Brighton remain 12th with four points separating them from the bottom three.
It took until the 21st minute for either goalkeeper to be tested for the first time, and even then it came from a cross as Mathew Ryan collected Dwight Gayle's delivery before getting to the ball ahead of the advancing Joselu at the second attempt.
Karl Darlow was then called into action at the other end five minutes later, but it was a simple save for the stand-in Newcastle keeper as he gathered Anthony Knockaert's shot from the edge of the area.
Any sights of goal continued to be half-chances at best in an uneventful opening 45 minutes, with Gayle seeing one shot blocked before Mikel Merino dragged the rebound across goal and wide of the far post.
Indeed arguably the best chance of the first half arrived just three minutes before the interval when Shane Duffy rose highest to meet a cross from Pascal Gross, heading his effort narrowly over the crossbar.
The second half provided more goalmouth action almost immediately as Ryan made a fine save to tip Isaac Hayden's deflected shot wide of the target just four minutes after the restart.
Brighton responded with a good spell of possession which saw Davy Propper threaten twice in quick succession, but they needed Ryan in form again shortly before the hour mark when he parried Gayle's header away from goal.
Joselu then failed to make the most of two shooting chances in quick succession before Brighton again threatened from a corner, this time Lewis Dunk seeing his header kept out by Darlow.
Neither side could find a way through in the closing stages, though, as they were forced to settle for a point apiece, leaving Newcastle with just one win from their last 12 outings and Brighton with only one from 10.
The Seagulls have now also scored only one goal in their last six matches, although they remain 12th with a four-point cushion to the relegation zone.
Newcastle (4-4-2): Darlow; Yedlin, Lascelles, Clark, Dummett; Ritchie (Perez, 72'), Hayden, Merino (Shelvey, 76'), Atsu; Joselu (Murphy, 84'), Gayle
Brighton (4-4-1-1): Ryan; Bruno, Duffy, Dunk, Bong; Knockaert, Stephens, Propper, March; Gross; Murray (Hemed, 62')