Chelsea and Tottenham Hotspurs earned three points but Liverpool were shocked by Burnley.
Chelsea scored twice in the last 10 minutes to beat Watford 2-1 in the Premier League on Saturday and earn their second victory of the season.
Watford's Etienne Capoue smashed a swerving shot past keeper Thibaut Courtois and into the top corner of the net after 55 minutes following a cross from the right by Adlene Guedioura.
Chelsea equalised 10 minutes from time, substitute Michy Batshuayi following up to tap the ball home for his first goal for the club after Eden Hazard's fierce shot was saved by Heurelho Gomes.
Substitute Cesc Fabregas then released Diego Costa with a sublime pass and the striker finished calmly three minutes from the end to seal victory for Antonio Conte's team.
Burnley stun Liverpool 2-0 with classy double
Promoted Burnley enjoyed their first win on the club's return to top flight after strikers Sam Vokes and Andre Gray produced superb first-half goals to give them a 2-0 Premier League win over Liverpool on Saturday.
Fans at Turf Moor had barely settled in their seats when Vokes beat goalkeeper Simon Mignolet with a rasping shot on the turn in the second minute after Gray found him on the edge of the penalty area.
Gray celebrated his first Premier League goal, cutting inside two markers and unleashing a crisp low shot from 18 metres which beat Mignolet at the near post after excellent work from Belgium midfielder Steven Defour.
Missing new signing Sadio Mane due to a shoulder injury, Liverpool were a pale shadow of the side that earned a 4-3 win at Arsenal on the opening day of the season. For all their possession, the visitors were reduced to sporadic long-range efforts against a well organised Burnley defence.
Wanyama strikes late to earn Spurs victory
Victor Wanyama grabbed a late goal, his first for the club, to earn Tottenham Hotspur a 1-0 Premier League victory over London rivals Crystal Palace on Saturday.
Spurs dominated the first half but Palace goalkeeper Wayne Hennessey made three fine saves to keep the visitors in the game.
Palace midfielder Yohan Cabaye missed a good chance on the hour, blazing a shot wastefully over the bar after being teed up by Spurs old boy Andros Townsend.
Spurs striker Vincent Janssen also spurned an excellent opportunity when he shot wide after being sent clear by a fine pass from substitute Dele Alli but Wanyama headed in from close range following a corner to seal the points seven minutes from time.
Everton fight back for 2-1 win at West Brom
Goals from Belgium forward Kevin Mirallas and midfielder Gareth Barry steered Everton to a 2-1 Premier League win at West Bromwich Albion on Saturday after Gareth McAuley had given the hosts an early lead.
It was the first taste of success for Everton's new coach Ronald Koeman, whose side fell behind after Northern Ireland defender McAuley stole in at the far post to head home a Craig Gardner corner.
Everton enjoyed the lion's share of the possession in the opening period and made it count on the stroke of halftime when Mirallas beat goalkeeper Ben Foster with a slick finish after incisive passing by Barry and Ross Barkley.
Everton looked a different side after fit-again striker Romelu Lukaku came on as a first-half substitute and Barry capped a memorable afternoon when he nodded in the winner on the hour after Mason Holgate's touch fell kindly for him.
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