Albion went into the game knowing a win would move them six points clear of danger with just two games remaining after Cardiff's loss at Fulham earlier on Saturday but they struggled to make any kind of impact in the first half.
Newcastle took a deserved lead on 18 minutes when an unmarked Perez lashed the ball home from close range after Salomon Rodon knocked the ball down into his striker partner's path with his chest.
The visitors were thoroughly dominant in the opening 45 minutes but Brighton improved after the break, in part due to the introduction of Solly March.
The Seagulls managed to level matters with 15 minutes left to play as Gross, arriving from deep, headed the ball past Martin Dubravka in the Newcastle goal with Glenn Murray providing the assist.
Murray could have won the game for Brighton late on after rising to meet substitute Anthony Knockaert's cross but he could only head the ball over the bar.
Brighton take on Arsenal and Manchester City in their final two games, but they may well have done enough to secure survival with the point against Newcastle as a vastly superior goal difference to Cardiff means the Bluebirds will have to win both of their remaining games to move above Albion.