Wilfried Zaha's first-half penalty looked to be enough to secure the hosts all three points in the M23 derby, before the late drama unfolded in south London.
Tariq Lamptey was adjudged to have pulled down Batshuayi in the box after 19 minutes, with Zaha keeping his cool to send goalkeeper Mat Ryan the wrong way from the spot.
The goal was Palace's only meaningful foray forward of an opening period in which Albion trio Adam Lallana, Yves Bissouma and Ben White each lashed wide at the other end.
Brighton remained the more threatening after the restart and top scorer forward Neal Maupay was twice denied early in the second period.
The Frenchman's deflected shot on the turn was kept out on the line by Eagles goalkeeper Vicente Guaita before he wasted a golden chance to level by delaying his shot and being blocked by Joel Ward having been slipped in by Lallana.
In between those opportunities, on-loan Chelsea man Batshuayi had a strike chalked off for offside, although Palace opportunities were almost non-existent.
But a battling display from the Seagulls was rewarded in second half stoppage time, as Mac Allister found the net via a deflected effort inside a crowded Palace penalty box.
Lewis Dunk then deservedly saw red for a rash challenge on Gary Cahill as Graham Potter's men searched for a last-gasp winner, but to no avail.
Brighton left it late to grab a 1-1 draw at Crystal Palace on Sunday with substitute Alexis Mac Allister grabbing his first-ever Premier League goal at Selhurst Park.