Liverpool left it late to beat Wolves 1-0 thanks to Divock Origi's 94th minute winner. Newcastle get their first win of the season.
Wolves 0-1 Liverpool
It was set to be a frustrating goalless draw for the Reds at Molineux, that was before Origi scored a very late winner to send Jurgen Klopp's side above Chelsea in the league table.
After a first half with very few chances at either end, Liverpool took a stranglehold in the second, creating plenty of good scoring chances.
One of those saw Diogo Jota round Wolves goalkeeper Jose Sa, carry the ball towards the net, only to fire his shot straight at Conor Coady who blocked on the line from six-yards out.
Wolves didn't get anything going in attack and were trying to hold on for a draw, but Origi's late goal came as a deserved winner for the visitors.
Newcastle 1-0 Burnley
Newcastle got their first win of the season by beating fellow strugglers Burnley 1-0, with Callum Wilson's first half goal separating the sides.
The goal came after Nick Pope dropped the ball, claiming to be fouled, before Wilson fired the ball into the roof of the net.
Burnley found it tough to create chances, losing attacking impetus after Maxwell Cornet went off injured in the first half.
The result moves Newcastle off the foot of the table and level on points with Burnley.
Southampton 1-1 Brighton
It was a case of de ja vu for Brighton, who scored a late equaliser for the second game in a week while playing with 10-men after losing a player to injury after making their three substitutions.
Southampton took the lead in the first half thanks to Armando Broja, but failed to cause their visitors many issues afterwards.
Leandro Trossard was taken off injured after Graham Potter had made all of his substitutions, but the Seagulls scored a late-late equaliser in the 98th minute through Neal Maupay again.
The draw leaves Southampton 14th and Brighton 9th in the Premier League table.