Mo Salah, the league's top scorer last year, scored the first-half winner to give Liverpool nine points from three matches after Manchester City's spotless start to their title defence was halted by a 1-1 draw at newcomers Wolverhampton Wanderers
Mohamed Salah struck again to ensure an underpowered Liverpool maintained their perfect early-season record in the 1-0 win over Brighton and Hove Albion at Anfield and climbed to the top of the Premier League Saturday.
Salah, the league's top scorer last year, scored the first-half winner to give Liverpool nine points from three matches after Manchester City's spotless start to their title defence was halted by a 1-1 draw at newcomers Wolverhampton Wanderers.
On a day when Arsenal earned their first win under Unai Emery, a 3-1 victory over West Ham United, the two title favourites, while far from their best, both dominated their matches but with very different outcomes.
City, who won their first two games of the season in fine style, again largely controlled affairs against Championship winner Wolves at Molineux but still had to come from behind to earn a point against Nuno Espirito Santo's impressive side.
Wolves had gone ahead fortuitously after the break with Willy Boly's diving header actually going in off his arm only for Aymeric Laporte to then equalise with a header, his first goal for City.
The champion hit the woodwork three times, once through Raheem Sterling, whose thunderbolt was tipped brilliantly on to the woodwork by Rui Patricio, and twice from Sergio Aguero, whose free kick struck the crossbar in the dying seconds.
Manager Pep Guardiola felt his side had been let down by fragile defending but reckoned it was still a good point against newcomers who had demonstrated why they can still thrive in the top flight.
In the day's late game, though, Salah demonstrated the clinical edge City had earlier lacked with his slide rule left-foot finish handing the edge to Liverpool.
It earned a lacklustre Liverpool a two-point lead over unbeaten City and Bournemouth, although Chelsea, Watford and Tottenham Hotspur all have chances to join them on nine points in matches to be played Sunday and Monday.
Arsenal prevailed after two defeats under Emery but only after Marko Arnautovic's first-half goal for West Ham prompted brief thought that the home side might lose their first three league matches of the season for the first time since 1954-55.
Arsenal, though, responded quickly with a goal from Nacho Monreal, before a second-half own goal from Issa Diop and a Danny Welbeck clincher in injury time left the Hammers still searching for a first point under new boss Manuel Pellegrini.
Emery, reckoning that it was an important win for the fans, dismissed rumours of a row with Mesut Ozil, saying the midfielder was not on duty because of illness.
It was the worst start by a West Ham manager since Avram Grant lost his opening four league games in 2010-11.
Bournemouth and Everton maintained their unbeaten starts to the season in a dramatic match at Dean Court in which both sides ended with 10 men.
Everton's new Brazilian strike hero Richarlison was dismissed for a headbutt aimed at Adam Smith just before the break while Smith himself was sent off for a second half foul on Theo Walcott.
The home side then fought back after Walcott and Michael Keane had put Everton two up, with goals in the last 15 minutes from Josh King, from the penalty spot, and Nathan Ake.
Southampton's difficult start continued with Harry Maguire's stoppage-time winner seeing Leicester City earn a 2-1 comeback win, a victory that will have brought much pleasure to visiting manager Claude Puel on his return to his former club.
Southampton, who have won just once at home in the Premier League this year, also had midfielder Pierre-Emile Hojbjerg sent off for two yellow card offences.
Liverpool 1 (Salah 23) Brighton 0
Arsenal 3 (Monreal 30, Diop 70-og, Welbeck 90+2) West Ham 1 (Arnautovic 25)
Bournemouth 2 (King 75-P, Ake 79) Everton 2 (Walcott 56, Keane 66)
Huddersfield 0 Cardiff 0
Southampton 1 (Bertrand 52) Leicester 2 (Gray 56, Maguire 90+2)
Wolves 1 (Boly 57) Man City 1 (Laporte 69)
Watford v Palace, Fulham v Burnley and Newcastle v Chelsea