The match was barely four minutes old when Liverpool took the lead. A raking pass out to the right saw Mohamed Salah isolated against Marc Cucurella and the Egypt international weaved one way and then the other before cutting back for Jordan Henderson to plant a side-foot finish past Robert Sanchez.
Liverpool lost Naby Keita, who recovered quickly from being carried off on a stretcher last weekend to start, to injury but his replacement Alex Oxlade-Chamberlain made an immediate impact.
Within five minutes of coming on he provided the inviting cross for Sadio Mane to head home from seven yards and make it 2-0.
Liverpool thought they had a third when a backpass put goalkeeper Robert Sanchez under pressure under his own crossbar and Mane blocked his clearance over the line. However, VAR ruled the ball had come off his hand after bouncing up off his body.
And the hosts were hit with a double blow when Enock Mwepu pulled a goal back for Brighton when he whipped a brilliant angled effort up and over Alisson.
There was much less fluency in Liverpool’s play after the break as Brighton pushed them back, sensing they were in with a chance.
And the equaliser deservedly came in the 65th minute when former Liverpool midfielder Adam Lallana teed up Leandro Trossard to fire past Alisson.
Scroll down and click through to see Logan MacLeod's player ratings
9. Adam Lallana - 7
Missed a massive opportunity in the first half and should have made it 2-2. Made amends for the miss by setting up Trossard's goal. Won a lot of tackles in the middle of the park. Always a leader on the pitch and will be delighted with salvaging a point. Walked off to a standing ovation at Anfield.
10. Enock Mwepu - 7
Scored again! It was an UNBELIEVABLE effort from the Zambian to lob Alisson from 25-yards out. Two goals in a week. He's taking his opportunity every game he plays. Got into dangerous areas thanks to his running in behind.
11. Leandro Trossard - 7
Acted as a false nine, dropped into space and kept the ball well. Showed some really nice dribbling throughout, most notably when he beat a few men and created a good chance for Mwepu. Repaid the manager's faith to start him up front by scoring the vital equaliser. Silenced the Anfield crowd with that goal. Very composed finish.
12. Alexis Mac Allister - 7
On for Bissouma in the 60th minute. Sat in a deeper midfield position and sprayed some nice balls about. Also got stuck in and won the ball back. Good little 30-minute cameo from the Argentinian as Brighton dominated the second half.