A Diogo Jota goal looked to have secured a win for the champions, only for the pitchside monitor review to deem Andy Robertson kicked Danny Welbeck’s foot and Pascal Gross made no mistake from 12 yards.
The defending champions still moved a point clear at the top of the table with 21 points from 10 games while Tottenham, who play at Chelsea on Sunday, have 20 points from nine.
Aaron Connolly wasted a great chance to put Brighton ahead in the 10th minute when he was put through clear on goal by Neal Maupay but with only Alisson Becker to beat he placed his shot wide.
The home side had an even better opportunity 10 minutes later when Liverpool right-back Nico Williams brought down Connolly in the box, but Maupay put his penalty kick well wide.
Having had those two let-offs, Liverpool thought they had taken the lead when Firmino fed Salah, who burst goalwards and poked the ball past Mat Ryan. But VAR ruled the Egyptian had been in an offside position.
Juergen Klopp took Williams off at the break, bringing Jordan Henderson off the bench in a move that brought a more familiar confidence to the champions' play.
The decisive/opening goal came on the hour when Andy Robertson fed Salah, who laid off to Jota, who in turn veered across the top of the penalty area, creating space for a low shot which he squeezed into the bottom corner. It was his ninth goal of the season in all competitions.
Liverpool, who face Ajax in the Champions League on Tuesday, suffered a blow when James Milner had to go off with what appeared to be a hamstring injury.
Sadio Mane had a headed effort ruled out for offside seven minutes from the end, before the late Brighton equaliser.
Additional reporting by Reuters.