Roberto De Zerbi's team went ahead at the Amex after just 20 minutes when Alexis MacAllister had his pocket picked by Simon Adingra, who then caught Alisson off-guard with a tame effort from distance.
However, the visitors surprisingly managed to go in at half-time ahead. In the 40th minute, Salah tucked the ball into the far corner from inside the box, rounding off an excellent team move. Just five minutes later, Liverpool's high press caught the Brighton defence napping and Dominik Szoboszlai was dragged to the ground. Into first-half stoppage time, Salah stepped up and tucked the spot-kick away with aplomb.
Jürgen Klopp's men were mostly in control in the second half until another defensive error, this time from the normally dependable Andy Robertson, allowed Lewis Dunk to thigh home Solly March's freekick with 15 minutes left on the clock.
As Liverpool pass up an opportunity to move second, here are five talking points from the game.
1) A real tactical battle
When facing Brighton, not only are you taking on a side filled with highly skilled technicians, but you’re also facing a master tactician in De Zerbi who has the agility to cater his game plan to any opponent.
Clearly, Jürgen Klopp had identified this and altered his game plan accordingly. In the first half, without the ball, the Reds lined up in a 4-4-2 formation. With it, it was much more fluid.
With Trent Alexander-Arnold returning to the team and stepping into midfield in a much more natural way than Joe Gomez, this allowed the Reds to maintain superiority in midfield while Harvey Elliott’s surprise inclusion allowed Mohamed Salah to take up a more central position.
2) Salah dropping deep
The tactical tit for tat produced one surprise in the first half: Salah playing as a number ten.
With Darwin Núñez leading the line, the Egyptian dropped into pockets where many fans have probably never seen him before, even at one point coming deep to try to collect the ball from Alisson.
Salah is in a rich vein of creative form, but wasn’t quite able to provide the killer pass from the middle. That didn’t stop him from scoring two first-half goals, though.
3) Mac Allister needs help in the “six”
In the second half, Ryan Gravenberch’s introduction saw a return to a more typical shape, with Dominik Szoboszlai dropping deeper to lend a hand to Alexis Mac Allister who, not for the first time this season, didn’t look most comfortable at the base of midfield.
For Brighton’s opening goal - although given a poor pass by Virgil van Dijk - he was caught on his heels and surrendered possession at a time when he was practically the last line of defence. This happened twice in one half against Wolverhampton Wanderers, too. There, he was hooked at half-time.
When the Reds are in the ascendency, his neat passing in tight areas is an asset in helping the side maintain momentum. However, it’s becoming increasingly clear that his best work is done in the opposing half.
4) Costly defensive errors
In a game with few clearcut chances for either team, Brighton’s goals came as a result of Liverpool’s own doing.
By his usual high standards, Alisson was made to look rather silly by Simon Adingra’s opening goal. He lost his bearings when Alexis Mac Allister was robbed of possession and committed to the dive too soon with the ball not travelling at any great speed.
While it would be easy to point the finger of blame at either of these two, it was captain Virgil van Dijk who fed Mac Allister the pass when he had two players already breathing down his neck. Being alert is crucially important when playing out from the back and Van Dijk ought to know better.
And so should Andy Robertson. It was his poor defending that directly led to Dunk's equaliser. The Scotland captain seemingly pulled out from clearing Solly March’s free-kick at the near post, allowing Dunk to make it 2-2 at a time when Liverpool had felt largely in control of the game.
5) A thin bench
Compared to other areas of the field, Liverpool are well-stacked in attack. But today, with Cody Gakpo missing through injury and Diogo Jota suspended, Jürgen Klopp only had young Ben Doak at his disposal off the bench.
Darwin Núñez and Luis Díaz both had quiet days by their standards and, on any other day, couldn't have complained if they had been hooked off.
Instead, after being pegged back, the Reds never looked likely to grab the vital third goal.