Wilfried Zaha had given the hosts the lead from the spot with his eighth goal against the Seagulls and Jordan Ayex inexplicably missed a golden opportunity to double their lead.
However, when the Eagles failed to deal with a routine clearance over the top, it allowed Maupay to saunter through on goal and he deliciously lobbed Vicente Guaita.
The visitors had the chance to move top of the Premier League table with a win, yet despite failing to get all three points, it was Patrick Vieira who sank to his knees when the result was confirmed.
For Palace, the crushing blow will feel like a loss and they face Leicester back at Selhurst less than 24 hours after their bitter rivals.
The opening goal of the game came from a crunching tackle by Joel Ward and the impressive Conor Gallagher made the difference first of all, producing an incisive drive into the area where Trossard committed the foul to leave referee Andre Marriner with little option but to point to the spot.
It ensured Zaha could celebrate his 400th appearance for the club with a goal, his eighth against the Seagulls, after he sent Sanchez the wrong way to ensure there were no red faces in the Eagles camp having taken over penalty duties from usual taker Luka Milivojevic.
Steven Alzate was introduced for the visitors at the break and Potter's side came out with better intent as Lewis Dunk forced Guaita to tip over his header. Lallana also had an effort blocked but the home side wrestled back the initiative.
Gallagher was the architect for the latest shift in momentum with his relentless pressing too much for the south coast outfit, who looked to be running on empty with substitute Alzate and Welbeck forced off with injuries.
Palace had also made changes by this point and Edouard's replacement Christian Benteke put the game on a plate for Jordan Ayew with 14 minutes left but the Ghanaian side-footed wide with only Sanchez to beat to extend his goal drought to 35 games.
It would prove a crucial miss as not long after Shane Duffy headed straight at Guaita from Gross' free-kick, another chance was created by the German and this one was finished.
As the clock ticked into the 95th minute, Gross side-footed forward for Maupay, who had run away from his markers, and produced a clinical finish over the Palace goalkeeper to spark wild scenes among the travelling faithful.
Referee Marriner blew for full time straight after kick-off and James McArthur and Brighton goalkeeper Sanchez came to blows before Seagulls captain Dunk was given a volley of abuse by the home fans in the Holmesdale Stand as he left the pitch.
It produced ugly scenes but in the end both were left to reflect on what might have been with the visitors missing the chance to go top while Palace's momentum under Vieira slowed.