Liverpool held off a spirited Leicester City comeback to remain top of the Premier League table as Chelsea also maintained their unbeaten start to the season.
After goals from Sadio Mane and Roberto Firmino had given Jurgen Klopp's side a comfortable lead at half-time, Liverpool goalkeeper Alisson made a horrendous error to allow Leicester's Rachid Ghezzal score a consolation as the Reds won 2-1.
Chelsea ran out 2-0 winners at home to Bournemouth courtesy of substitute Pedro and Eden Hazard, ensuring they remain hot on the heels of Liverpool with only an inferior goal difference keeping them off the top of the table.
It was a mixed game for Aleksandar Mitrovic as his Fulham side drew 2-2 away to Brighton, scoring the Cottagers' second before conceding the penalty that led to the hosts' equaliser.
Andre Schurrle had given Fulham the lead but Glenn Murray scored twice in the second half for the Seagulls to reduce the two-goal deficit.
Adama Traore scored an injury-time winner for Wolves as they beat West Ham 1-0 - the Hammers are still without a point - while there was a late goal too for Southampton as Pierre-Emile Hojbjerg found the back of the net.
Danny Ings had earlier scored for the Saints as they completed a 2-0 victory away to Crystal Palace to secure their first win of the season.
The defeat for West Ham was their fourth in a row under Manuel Pellegrini, leaving them on zero points, while Wolves' win was their first in the top flight since February 2012.
Huddersfield were also seeking their first victory of the campaign and there were two goals in two minutes as they took on Everton at Goodison Park.
Philip Billing scored the opener for the Terriers but Dominic Calvert-Lewin bagged his third goal in two games to ensure a point for the unbeaten Toffees.