Albion led after 20 minutes but eventually had to work hard for an entertaining 2-2 draw.
The Seagulls forced a succession of early corners one of which appeared to be straight off the training ground and almost caught Liverpool out.
Pascal Gross played short to Solly March and his cross allowed Lewis Dunk to direct a header at goal.
Albion went ahead as Simon Adingra pressed Alexis Mac Allister and easily won the ball and was able to side-foot it past Alisson from outside the area to put the Albion in front.
March and Carlos Baleba both had excellent chances to put the Seagulls further ahead but both were thwarted.
Five minutes before half-time Albion lost possession near halfway line. Liverpool quickly recycled the play.
Luis Diaz and Darwin Nunez combined well, with a cross that Harvey Elliott let run across him. As the ball reached Mo Salah, he smashed the equaliser past Bart Verbruggen for 1-1.
Two minutes later, Verbruggen, similar to his error against Bournemouth, played a short pass to Gross who was on his heels.
Dominik Szoboszlai nipped in and Gross appeared to pull him down by the collar. After a quick VAR check, Salah put Liverpool ahead from the spot.
Albion and Liverpool were fairly evenly matched in the early stages of the second half although Liverpool could have wrapped it up when Szoboszlai lashed an effort against the bar with the goal gaping.
The Seagulls has a great shout for a penalty as Kaoru Mitoma raced into the area. His shot appeared to hit Virgil van Dijk on the hand but later it transpired that it had hit his thigh first.
Joel Veltman then released Adingra who cut inside and had just Alisson to beat but the Brazilian keeper made himself big as pushed the effort wide.
Albion got back into it after a fairly soft-looking challenge on March by Liverpool substitute Ibrahima Konate. March fired in a free kick and Dunk bundled the ball home for 2-2 with 12 minutes left
The final chance fell to Albion as Adingra rolled a pass to Joao Pedro who, from eight yards and with just Alisson to beat, blazed his shot over.
Albion stay sixth and have now been in the top six consistently since August, possibly the highest continuous position ever achieved by the club.
Next up in the Premier League, Albion travel to the Etihad to face out-of-form Manchester City on Saturday 21 October.
Brighton and Hove Albion remain title contenders.
