Recalled top scorer Maupay, back in Albion’s team after three substitute appearances, somehow squandered a golden opportunity with just eight minutes gone on a bitterly cold evening at the Amex Stadium.
Graham Potter’s Seagulls dominated the contest but, despite the best creative efforts of energetic star man Tariq Lamptey, failed to capitalise on a host of chances.
Lively Leandro Trossard and substitute Solly March each rattled the woodwork, while luckless Frenchman Maupay and Jakub Moder wasted further excellent openings.
The Sussex stalemate was a sixth draw during Albion’s lengthy run without victory but was sufficient to move them up a place to eighth, above Manchester United.
Lacklustre Leeds, who stay fourth from bottom, have never won on this ground and rarely looked likely to end that run as their difficult season continued.
Yet they would have snatched it had Seagulls goalkeeper Robert Sanchez not been alert to twice deny Tyler Roberts late on.
Bidding for a first win in more than two months, Albion boss Potter recalled striker Maupay, while Rodrigo and Raphinha were back to bolster Leeds’ attacking options.
Brighton began with far greater spark but could not illuminate their commanding first-half display with a deserved breakthrough, despite a raft of chances.
Lamptey, ably assisted by Trossard, was the tormentor-in-chief.
The rampaging right wing-back gave recalled Leeds defender Junior Firpo a torrid evening and almost had an early assist when Moder volleyed narrowly over.
Unmarked Mapuay should then have capitalised on Lamptey’s early enterprise but he somehow diverted a bouncing ball over the gaping goal after a right-wing cross was helped on by Pascal Gross.
Leeds, seeking only a third top-flight success of the campaign, were increasingly on the back foot and struggling to create when they did venture forward.
Marcelo Bielsa’s men wanted a penalty when Raphinha tumbled over the grounded Trossard before referee Craig Pawson dismissed appeals at the other end when visiting captain Liam Cooper diverted Lamptey’s deflected cross on to his own arm.
Leeds keeper Illan Meslier then superbly touched Trossard’s arrowing drive on to the outside of left upright, while Poland midfielder Moder later rattled the same post with an attempted cross and the unmarked Maupay volleyed off target.
Leeds defender Cooper again escaped being penalised following another possible handball in the 18-yard box and his side would have been relieved to trudge down the tunnel still level.
Unsurprisingly, Bielsa opted for changes at the break, withdrawing the booked Firpo and England international Kalvin Phillips in favour of Pascal Struijk and Jamie Shackleton.
Stuart Dallas eventually produced Leeds’ first attempt on target, a stinging drive which Sanchez – back from a one-match ban – pushed away 10 minutes after the restart.
Moder was then off target twice in quick succession at the other end before Sanchez was forced to repel a low effort from substitute Roberts with his feet following a Leeds breakaway.
Maupay’s misery was compounded in the 68th minute when he was replaced by Jurgen Locadia, a player who looked surplus to requirements during two loan moves and last scored a Premier League goal in December 2018.
Albion’s chances dried up a little after that and they were thankful Spaniard Sanchez kept out Roberts following a defensive lapse and again from the resulting corner.
The hosts had one final chance to claim all three points, but March’s low effort bounced back off the right post, before the final whistle brought a handful of boos from the frustrated home fans.