Goals from Pedro and Willain helped Chelsea see off a stubborn Rafael Benitez Newcastle side at Stamford Bridge in the Premier League.
Winger, Pedro opened the scoring with the help of a assist from David Luiz early on in the encounter.
A Ciaran Clark header shortly before half-time levelled matters in a keenly contested encounter.
The points were Chelsea’s, however, thanks to Willian’s curling strike 12 minutes into the second half.
Fourth-placed Chelsea pulled six points clear of Arsenal who lost to West Ham.
Newcastle will end the weekend in the relegation zone, a point behind 17th-placed Cardiff City.
Chelsea head to Arsenal next weekend, while Newcastle host fellow strugglers Cardiff City after travelling to Blackburn Rovers for an FA Cup third-round replay.
Table topping Liverpool returned to winning ways as Salah scored the winner from the penalty spot in the 50th minute after he was clumsily fouled by Pascal Gross.
Brighton did not manage a shot on target and Liverpool will now wait and see if title-rivals Tottenham and Manchester City can close the gap when they play on Sunday and Monday respectively.
Liverpool have 57 points from 22 Premier League games this season; in English top-flight history, only Preston (58 in 1888-89), Tottenham (59 in 1960-61), Chelsea (61 in 2005-06) and Manchester City (62 in 2017-18) have ever had more at this stage when adjusting to three points for a win.
Liverpool have conceded just 10 goals in their 22 league matches this season; only Chelsea in 2004-05 (eight goals) have ever conceded fewer after 22 matches in an English top-flight season.
Brighton manager Chris Hughton has lost more league games to Liverpool in his managerial career (seven defeats from seven meetings) than any other side. His sides have conceded 26 goals across those seven games.
This was Liverpool’s 50th clean sheet in the Premier League under Jurgen Klopp in their 128th match with the German in charge since his first in October 2015; 42% of those have come since Virgil van Dijk’s league debut in January 2018 (21 in 37 games since).
Brighton have now lost as many games at the Amex Stadium in all competitions this season (four of 12) as they did in the entirety of 2017-18 on home soil (four of 22 matches).
Liverpool forward Mohamed Salah has scored the opening goal in nine Premier League games this season, at least three more than any other player.
Brighton travel to Manchester United next Saturday before hosting West Brom in the fourth round of the FA Cup on Saturday, January 26. Liverpool are at Anfield for their next two Premier League matches as they host Crystal Palace on Saturday,