The Seagulls were the better of the two sides on the day, and could count themselves unlucky not to have won the game having created a number of chances which ultimately went begging — though Leeds also had opportunities of their own and came close to nicking all three points.
The result sees Brighton climb to 8th in the Premier League table, while Leeds remain 17th.
Story of the game
Coming into the match, Brighton manager Graham Potter made three alterations to the side that lost to Aston Villa last time out, with Robert Sanchez returning in goal, Joel Veltman coming in for Shane Duffy in defence, and Neal Maupay being reinstated up front as Adam Lallana dropped to the bench.
There were also three changes to Marcelo Bielsa's Leeds side after the 2-1 defeat at Tottenham Hotspur last weekend. Junior Firpo came in at left-back, but the most significant changes were in attack as Raphinha and Rodrigo returned to the starting line-up, replacing Mateusz Klich and youngster Joe Gelhardt respectively.
There was a good tempo to there match right from the off, with the hosts enjoying the better of the early chances. First, Marc Cucurella hung in a searching cross which just evaded the head of Maupay, and moments later Jakub Moder went close with a volley across goal.
It was Tariq Lamptey who put the cross in for that effort, and the wing-back turned provider once again when he beat Liam Cooper to the byline and delivered a low cross which found Maupay unmarked in the middle — however, with the goal gaping, the Frenchman somehow got under the ball and saw his effort flash over the bar.
That was a real let-off for the visitors, who had been second best thus far.
In fact, Leeds' best action of the first 15 minutes came courtesy of Raphinha, who twinkled-toed his way into the box under pressure from Moder and Cucurella before going down under a challenge from the latter, however referee Craig Pawson was unmoved in response to the Brazilian's claims for a penalty.
Brighton came close again when they worked the ball to Leandro Trossard on the edge of the box. The Belgian received the ball after good hold-up play from Maupay, set himself, and took aim at the far top corner, missing the target by the finest of margins as his effort clattered off the wrong side of the post and out for a corner.
On the 25-minute mark, a deflected free-kick from Raphinha found its way to the far-post where Dan James was lurking however, akin to Maupay's earlier opportunity earlier, a good chance went begging as the forward failed to get his contact with the ball right.
Trossard was given another opportunity to strike at goal when he was picked out well by Moder following a storming run down the right, however the eventual effort was straight at goalkeeper Illan Meslier.
Moder's running was causing serious problems for the visiting defence. Just moments later, the Polish international latched onto a loose ball in the box, and his resultant delivery ended up clipping the upright with Meslier and the Leeds back line perplexed having expected the ball to be crossed.
It was, surely, just a matter of time before the breakthrough came.
It should have come with just under 10 minutes of the half when Lamptey was released in behind and squared the ball for Maupay in the middle, however the striker again couldn't adjust his footing in time to direct his effort goalwards.
Goalless it somehow finished at half-time — the hosts had deserved more on the balance of play, but Leeds too were aggrieved not to have found the net, and the attacking impetus of both sides would surely show no signs of diminishing after the break.
Two changes at half-time from Bielsa — with Pascal Struijk replacing Firpo and Jamie Shackleton coming in for Kalvin Phillips — indicated he wasn't happy with his team's performance in the first-half, but Leeds were first to draw a save after the break when Stuart Dallas' long-range drive called Robert Sanchez into action.
There was a minor scare for the visitors when Moder's cross, which should have been claimed routinely by Meslier, was spilt by the goalkeeper with Maupay waiting to pounce, however 21-year old regathered the ball just in the nick of time.
Brighton were handed a brilliant chance to break the deadlock when a poor back-pass from Shackleton was latched onto by Moder, but the Pole didn't make good enough contact with the ball to direct it goalwards. He was handed another opportunity just moments later when Pascal Gross suppled him from the byline but, again, failed to test Meslier in goal.
Two big scares navigated, Leeds marched straight down the other end through substitute Tyler Roberts, and the forward eventually drew a good save from Sanchez. It was simply remarkable that, 70 minutes in, this match was still yet to witness a goal.
Lamptey was a constant worry for the visiting defence. With just over 15 minutes remaining, he robbed Adam Forshaw of possession and fed Moder on the edge of the area who then immediately slid the ball into Jurgen Locadia, but the striker's effort on the turn was pretty tame.
However, Lamptey bowed out just moments later, making way for Solly March, and the substitute came close to breaking the deadlock when he worked his way from right of the box to a more central effort and drew a fine save from Meslier with the resultant shot.
Roberts had been lively since his introduction from the bench, and was given a good chance when he received a neat back-heeled pass from Rodrigo in the area, but the forward couldn't sort his feet out in time to trouble Sanchez.
Brighton nearly shot themselves in the foot with just under 10 minutes remaining when a lazy pass from Adam Webster was pounced on by James. The forward got the ball to Rodrigo who got his shot away quickly, but Webster redeemed himself with a crucial block to divert the ball behind for a corner.
It then fell to Forshaw on the edge, whose effort was subject to a number of deflections and looked to be trickling in but for a good dive from Sanchez.
The match turned increasingly cagey as it headed into its final exchanges, but there was time for one more gilt-edged chance when Veltman worked the ball to March in the box. He shifted it onto his stronger left foot and took aim towards the near post, and it hit the upright before bouncing straight into the grateful grasp of Meslier.
Unlucky for the Seagulls, but that was just the order of things this evening, and all-square was how it finished — a result which, considering how the game played out, Leeds will be much more content with.
Takeaways from the match
End product costs Brighton two points
This was a match Brighton should have won — they had more of the ball than their opponents and created nearly twice as many shots (20 compared with Leeds' 11) but lacked that clinical touch in the crucial moments; just four of those efforts were on target.
Maupay in particular had an evening of mixed fortunes, constantly a handful for the visiting defence but failing to deliver when it really mattered.
Potter will be encouraged by his side's overall performance, but it's now eight winless for the Seagulls and this was a genuine opportunity to get three points on the board.
Leeds struggle to take control of the contest
This was a very different performance to the one we saw from Bielsa's side at Tottenham last weekend. They were on the back foot for the majority of the contest, sometimes enduring large spells camped in their own half, and it always felt as though they'd struggle to get a result whilst that was the case.
It's made all the more frustrating for the Yorkshire outfit due to the fact that when they did get forward they caused real problems for the Brighton defence, and came desperately close to nicking victory from the jaws of defeat in the second-half.
This match will leave much for Bielsa and his team to ponder; Leeds remain in the conversation at the bottom end of the table and will want to be initiating an ascent sooner rather than later.
Brighton & Hove Albion: Sanchez; Veltman, Dunk, Webster; Lamptey (March 76'), Gross, Bissouma, Moder (Sarmiento 81'), Cucurella; Maupay (Locadia 68'), Trossard.
Unused subs: Steele, Duffy, Richards, Mwepu, Lallana, Mac Allister.
Leeds United: Meslier; Llorente, Phillips (Shackleton 46'), Cooper; Dallas, Forshaw, Firpo (Struijk 46'); Raphinha, Rodrigo, Harrison (Roberts 63'); James.
Unused subs: Klaesson, Cresswell, McCarron, Jenkins, Klich, Gelhardt.
Referee: Craig Pawson
Following this draw here, Brighton travel to the capital to face West Ham United on Wednesday night.