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
1. Robert Sanchez - 6
Very fortunate to not have gifted Liverpool a goal to make it 3-0 after Mane closed him down on his own goal line - VAR ruled the striker had handled the ball into the net. Played a good ball into Cucurella which led to the Trossard equaliser. Protected well by his defence.
2. Joel Veltman 6
Let his man - Mane - get in behind to score a header from six-yards out. Will be disappointed with that. Other than that, was a relatively quiet afternoon. He kept his shape well and did what was needed.
3. Shane Duffy 7
Good block to deny Oxlade-Chamberlain from inside the box. Didn't have too much to do as was protected by his midfield. Couldn't do much about the two goals conceded. Solid next to Dunk. 7/10
4. Lewis Dunk - 7
Great last ditch block to stop Firmino from scoring a certain goal. Impressive covering to stop The Reds counter-attacking through Mane. Not much he could have done to stop the goals. Solid next to Duffy.