Trailing to Wilfried Zaha's first half penalty, Brighton avoided defeat in the most remarkable fashion.
With just seconds left at Selhurst Park, French striker Maupay punished a poor clearance from Palace keeper Vicente Guaita to leave the host stunned.
Brighton has been this season's surprise package and a victory in south London would have taken it into first place in the top tier for the first time in its 120-year history.
While Graham Potter's side was unable to achieve that lofty aim, stealing a point in the derby clash was sufficient consolation.
It sits sixth in the table, just one point behind leader Liverpool.
Born in the 1970s as a result of a spat between then Palace boss Terry Venables and his Brighton counterpart Alan Mullery, the Eagles and the Seagulls have an unusually bitter rivalry for two clubs located 45 miles apart.
Their meetings have been dubbed 'El Gatwicko' in a reference to the Gatwick Airport located between Selhurst Park and Brighton.
While few would mistake this curious grudge match for the intensity of the Manchester or Merseyside derbies, there was no doubting the passion of the Brighton players and fans as they celebrated at the final whistle.
It was cruel on Palace boss Patrick Vieira, whose side dominated for long periods but has just one win from its first six league games under the former Arsenal star.
When Zaha and Joachim Andersen combined to rip through the Brighton defence early on, Odsonne Edouard's shot lacked the power to beat Robert Sanchez.
Brighton showed only occasional signs of the penetrating play that has carried them up the table.
Leandro Trossard fired into the side-netting before Danny Welbeck raced through and shot straight at Guaita while appealing in vain for a penalty after a tug from Joel Ward.
It was Palace who took the lead in first half stoppage-time when Conor Gallagher's bold surge into the area was halted by a crude block from Trossard.
Zaha sent Sanchez the wrong way with his penalty to make it eight career goals against Brighton for the Ivory Coast forward.
Guaita tipped over Lewis Dunk's looping header from Marc Cucurella's free-kick soon after the interval.
Jordan Ayew should have put the result beyond doubt with 15 minutes left when Christian Benteke's pass put him through on goal, but the Ghana forward shot just wide.
That proved a crucial miss as Brighton escaped in the final minute of stoppage-time.
Guaita's poor goal-kick was seized on by Pascal Gross and he lofted a pass beyond the out-of-position Palace defence towards Maupay, who sprinted to the edge of the area and guided a fine finish over the Palace keeper.
Brighton's wild celebrations left Palace fuming and James McArthur clashed with Sanchez as a blue flare was thrown onto the pitch from the jubilant Seagulls fans.