The Seagulls have now failed to achieve victory in eight successive league outings in the Premier League after a fantastic start to the season left the club competing at the top of the table.
Manager Graham Potter could only watch as the side hit the woodwork on three occasions.
Leeds appeared overpowered by Brighton's robust football, especially in the first half, although grew into the game after the break and came close through Tyler Roberts twice in the closing stages.
The result sits Albion eighth place despite the winless run, whilst Leeds remain just one place above relegation - with just two wins across 13 fixtures this season.
Story of the match
Brighton opened the match with aggression, seeking to strike early and grasp a lead to protect against their struggling opposition.
This so nearly came after just five minutes, with the energetic Tariq Lamptey impressing once again and planting a precise cross into Neal Maupay's path, who scuffed a simple shot over the bar from yards out.
Leeds grew into the half after being somewhat overpowered in the initial period, gaining a foothold and levelling possession as attempts were made to bypass the Brighton backline.
Albion manager Potter cut a stern figure on a spiteful evening on the South Coast, clearly discontented with yet another performance brimming with hope but lacking a decisive touch.
After the break, with the teams level, Leeds improved and started to find success stretching the home defence and initiating forward thinking moves.
Stuart Dallas provided United's first shot on target of the affair after 55 minutes, sending a looping strike into the centre of the goal but failing to thwart the Robert Sanchez, who parried the shot away from danger.
Despite their best efforts, Leeds ultimately found themselves falling into a pattern reminiscent of the first half, and often had multiple bodies placed in the defensive half with incentive on preventing the Brighton press.
This approach was largely effective, with the home side only finding the target twice despite 16 efforts throughout the game.
Leeds yet to lose back-to-back fixtures in the division this season and were defensively solid and resilient in taking a point from the AMEX before a vital week in the division.
Lamptey a serious player
Tariq Lamptey. The young full-back has captured the attention of fans across the country with his ferocious pace and deft movements, serving as an offensive focal point down the right flank.
His creative aptitude was consolidated by five chances created during the first half alone; should form be maintained - and maybe bettered in the coming months - Lamptey will no doubt become a prominent figure in English football.
Clinical talisman paramount
Old patterns resurfaced on a harsh winter afternoon in the Premier League. Yet again, Brighton exhibited attacking incentive and yet again, the clinical touch agonisingly evaded the side.
After four victories from a possible five to commence the campaign, Brighton have now gone eight matches without claiming three points - albeit, only twice have they been beaten in this period.
Hopes high despite winless run
Brighton and Leeds have had contrasting success across the opening stages of the 21/22 campaign, with Albion settling in the upper echelons of the table whilst injury-stricken United flirted with the relegation places.
The point differential is now closing as the season enters the mid-point, but the difference in quality and confidence was apparent.
Brighton have faith in their ability, and their manager, and will no doubt find that elusive victory in their grasp once again if levels of cohesion and fluidity are maintained.
Next time out
Brighton return to the field one day later, with a challenging fixture in London against West Ham United the contest - the respective sides have both done well to set themselves in good stead thus far, and a ferocious fixture is expected.