Marcus Rashford and Marouane Fellaini came off the bench to score as Manchester United’s perfect start to the season continued with a 2-0 victory against Leicester.
Those goals saved the blushes of Romelu Lukaku, who had seen a penalty saved by Kasper Schmeichel in the 53rd minute.
Raheem Sterling struck a deflected added-time winner to give Manchester City a hard-fought 2-1 victory against Bournemouth.
The England international was then sent off by referee Mike Dean for celebrating among the away fans.
Bournemouth took a 13th-minute lead in spectacular fashion when Charlie Daniels latched onto a loose ball to arrow a drive past Ederson and in off the crossbar from an acute angle.
But City were level soon after as Gabriel Jesus taking a swift free kick to David Silva, whose slide-rule ball back to the Brazilian was converted with ease by the forward.
Pep Guardiola’s side toiled but didn’t make a breakthrough until deep into added time when Sterling scored from close range before being dismissed.
Swansea condemned Crystal Palace to a third straight defeat as they ran out 2-0 winners at Selhurst Park.
Tammy Abraham, on loan from Chelsea, scored his first goal for the club and Swansea’s first goal of this league season shortly before half-time.
Jordan Ayew added a second three minutes after the break to strengthen the visitors’ lead.
Palace, responded well and created several opportunities but were unable to find a breakthrough.
Newcastle grabbed a much-needed victory to ease the pressure on manager Rafa Benitez, winning 3-0 against West Ham.
Three of Newcastle’s summer signings combined for the opening goal in the 36th minute as Mikel Merino picked out Christian Atsu, who squared for Joselu to score.
Ciaran Clark headed home the second off the post in the 72nd minute before Aleksandar Mitrovic sealed a deserved win with an 86th minute goal.
That defeat leaves West Ham still searching for their first point of the season having conceded 10 goals in their first three games.
Brighton missed a golden opportunity to claim a first ever Premier League win as they drew 0-0 with 10-man Watford at Vicarage Road.
The hosts were reduced to 10 men when Miguel Britos was dismissed for a wild challenge on Anthony Knockaert in the 24th minute.
The Brighton man had earlier struck the post with a curling effort, while Tomer Hemed also hit the post with a shot in the 37th minute.
Brighton record signing Jose Izquierdo was given his debut as a late substitute but the Colombian winger was unable to make the difference.
Huddersfield’s perfect start to the season came to an end as they were held to a goalless draw by Southampton.
David Wagner’s side had already beaten Crystal Palace and Newcastle but they couldn’t find a way past Mauricio Pellegrino’s men