Dominik Szoboszlai's stunning late free-kick saw Liverpool edge out Arsenal to make it three wins out of three to start the Premier League season.
In a battle between the teams that finished first and second last season there was little between the two teams until Szoboszlai, who again started at right-back to cover for injuries, stepped up to whip an all but unstoppable free-kick into the top left-hand corner in the 83rd minute.
Arsenal introduced new signing Eberechi Eze as a second-half substitute but did not produce enough of a goal threat.
Manchester City fell to a second straight Premier League defeat as Brajan Gruda's late strike gave Brighton a 2-1 come-from-behind win at the Amex Stadium.
City looked comfortable after Erling Haaland marked his 100th English top-flight appearance with his 88th goal, but failed to build on the advantage and paid the price.
James Milner scored from the spot against his former club in the 67th minute after Matheus Nunes handled before Gruda won it in the 89th minute.
West Ham lifted some of the pressure on Graham Potter as three late goals gave them a 3-0 win at Nottingham Forest.
Captain Jarrod Bowen fired West Ham in front in the 84th minute, and Forest capitulated as Lucas Paqueta scored from the spot - kissing the badge amid speculation linking him with a move away - before Callum Wilson got his first Hammers goal.
While Potter earned just his sixth win in 23 as Hammers boss, the late collapse will add to the tension ahead of clear-the-air talks between Forest boss Nuno Espirito Santo and owner Evangelos Marinakis planned for the international break.
