Captain Jordan Henderson fired the Reds ahead from 18 yards moments after Alisson had denied Solly March at the other end following Leandro Trossard’s defence-splitting pass.
Yves Bissouma, making his first start since 19 September after recovering from a knee injury, then had an effort tipped on to the post before Sadio Mane headed Liverpool into a 2-0 lead after a cross by Alex Oxlade-Chamberlain, on for the injured Naby Keita.
Brighton’s comeback started through Enock Mwepu’s first Premier League goal, a stunning attempt from 25 yards which deceived Alisson.
Graham Potter’s side were impressive and they equalised when Trossard slotted home after an assist by former Liverpool player Adam Lallana.
In an entertaining game, Mane and Mohamed Salah both found the back of the net either side of half-time, but both attempts were ruled out for handball and offside respectively.
In a tense finale, Brighton thought they had won it when Trossard scored in front of The Kop, but it was ruled out for offside.
Liverpool’s defence comes under scrutiny
Jurgen Klopp’s side head into November with their unbeaten record intact, but the Liverpool boss will be unhappy with how his side threw away a healthy lead – and were left hanging on for a point.
For long periods on Saturday the Reds sat top of the table as Chelsea, who had started the day at the summit, were held by Newcastle before scoring three quick goals to move three points clear of Liverpool.
While the Reds were once again impressive going forward, they were vulnerable at the back from start to finish as Brighton got in behind the defence on numerous occasions.
The loss of Keita, who suffered heavy bruising in the 5-0 hammering of Manchester United last weekend, to another injury will be a concern for Klopp with a busy November to begin against Atletico Madrid in the Champions League on Wednesday.
As for Brighton, they continue to impress under Potter.
Having won at an empty Anfield last season, they relished the full house surroundings, carving out nine attempts of which six were on target.
They are moving in the right direction and now have 16 points from 10 games – six more than after the same number of games last season.
Potter, meanwhile, will be confident his side can return to winning ways with matches against Newcastle, Aston Villa and Leeds on the horizon.
The England midfielder walked up to The Kop at full-time to applaud supporters who in turn chanted his name.