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.
But Rashford, who had been replaced in the starting XI by Anthony Martial, came on for Juan Mata in the 67th minute and scored three minutes later.
The England international kept his composure to fire home a Henrikh Mkhitaryan corner from close range after losing his marker.
Then Fellaini knocked one in with his knee in the 82nd minute following good work from Jesse Lingard on the left wing.
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 extended their unbeaten start to life in the Premier League with a goalless draw at home to Southampton.
The Terriers launched their first top-flight season in four decades with two straight victories and despite being held by the Saints in an entertaining stalemate, head coach David Wagner will be delighted with his side's return going into the international break.
Both sides had chances to snatch the points. Steve Mounie and Thomas Ince went closest for the home side, while Town skipper Tommy Smith cleared Ryan Bertrand's late header off the line.
Mauricio Pellegrino's side, who also extended their unbeaten league record, arrived full of intent but will be grateful to have left the John Smith's Stadium with a point.