Hakim Ziyech fired the European champions into a first-half lead at the Amex Stadium with a low strike against the run of play.
But the third-placed Blues were second best for much of the evening and could have few complaints about stand-in Seagulls skipper Adam Webster levelling with a thumping 60th-minute header.
Chelsea topped the table as recently as the start of last month but have spectacularly fallen out of title contention having now won just two of their nine top-flight outings since.
Thomas Tuchel’s men struggled for cohesion and fluidity throughout their visit to Sussex, with record signing Romelu Lukaku once again ineffectual before being withdrawn 10 minutes from time.
The out-of-sorts Blues, who suffered a damaging weekend loss at leaders on Manchester City, are now 12 points adrift of top spot, having also played a game more.
Indeed, the west London club may soon be looking over their shoulders as the plethora of recent postponements have left top-four rivals Arsenal and Tottenham with a number of games in hand in the battle for Champions League qualification.
High-flying Brighton remain ninth following their 11th draw of a campaign in which they have lost just four times in the league.
Tuchel responded to Saturday’s 1-0 loss at the Etihad Stadium by recalling Jorginho, Mason Mount and Callum Hudson-Odoi.
The personnel changes initially failed to have the desired effect as Brighton began with far greater purpose, prompting Tuchel to grow increasingly exasperated on the touchline.
But, despite a poor start littered with sloppy errors, the German was given reason to smile in the 28th minute as the visitors edged ahead against the run of play.
Moroccan Ziyech worked space just outside Albion’s box before unleashing a low left-footed drive which caught out Seagulls goalkeeper Robert Sanchez and flew into the bottom right corner.
The bolt from the blue almost certainly should have been saved by Sanchez and briefly stunned the vocal home crowd.
Brighton head coach Graham Potter who spent part of his pre-match press conference brushing off speculation linking him with the vacant Everton job, had sprung a surprise with his team selection by dropping Leandro Trossard and Neal Maupay.
The attacking pair had contributed more than half of Albion’s league goals this term and, as they watched on from the bench, Potter’s side could not turn first-half promise into an attempt on target.
Jakub Moder flashed their best attempt wide early on, while they could have been further behind had Hudson-Odoi not wastefully fired over just before the break.
Danny Welbeck, who claimed a late equaliser when Brighton drew 1-1 at Stamford Bridge less than a month ago, was given the job of leading the hosts’ attack.
The former England forward was lively on his first league start since suffering injury in September and skewed wide of the left post just after the restart.
With Dan Burn getting the better of a bruising battle with Lukaku and former Chelsea man Tariq Lamptey a constant menace down the right, Brighton continued to cause problems for the away side and their persistence was rewarded with a deserved leveller on the hour mark.
Alexis Mac Allister forced a fine save out of Kepa Arrizabalaga before his inviting delivery from the resulting corner was emphatically nodded home by centre-back Webster.
Potter issued a signal of intent by introducing Trossard and Maupay in the immediate aftermath of the equaliser.
Chelsea came back into the game after being pegged back but the two sides created little of note in the closing stages.
On a rare occasion when Lukaku escaped Burn, his effort was turned wide by Sanchez, before he was withdrawn.
Mateo Kovacic, Timo Werner and Kai Havertz were thrown on but could not help carve out a winner on another frustrating occasion for Tuchel.