Ayoze Perez put Newcastle in front in the 18th minute with a fine finish and the home side rarely offering anything in response for the remainder of the half.
Brighton did improve after the break and got their reward after 75 minutes when Pascal Gross headed in their first goal in eight matches in all competitions to equalise, much to the relief of the home supporters.
Brighton striker Glenn Murray had a glorious late opportunity to win the match, but headed over from close range.
With Arsenal and Manchester City to play, Brighton are not safe, but possess a far superior goal difference to Cardiff, who now need to win both their final games to have a chance of survival. Newcastle remained comfortable in 13th.
"There was a big relief for all of us," Gross told the BBC. "We pushed for the second but unfortunately that didn't happen. Two games left, we will see how it ends."
Newcastle controlled the early stages and deservedly took the lead through Perez, who lashed home Salomon Rondon’s chest layoff, and that was Perez’s last involvement in the match as he limped off soon after.
Fabian Schar was denied by a smart save from Brighton goalkeeper Mat Ryan and the hosts failed to muster a shot on target in the first half.
There was much more threat from Brighton after the interval and Shane Duffy headed just over.
Brighton’s persistence finally paid off as Gross headed in Murray’s knockdown from close range before Murray passed up the opportunity to snatch all three points with two minutes left.
"They were aggressive and they were fighting to avoid relegation," Newcastle manager Rafa Benitez told BT Sport. "We needed to keep the ball better and our counter-attacks were not good.
"They were desperate to win so we need to understand the context of the game."
(Reporting by Peter Hall, editing by Ed Osmond)
