Early leaders Everton maintained their perfect start to the season with a 2-1 win at Crystal Palace, while a penalty in the 10th minute of stoppage time gave Manchester United a 3-2 win at Brighton in the Premier League on Saturday.
Chelsea fought back from 3-0 down at the break to earn a 3-3 draw at West Bromwich Albion, while Danny Ings grabbed the winner as Southampton got their first win of the campaign at struggling Burnley.
Carlo Ancelotti's Everton made it three wins out of three, winning with a penalty at Selhurst Park that had Palace manager Roy Hodgson fuming after the match.
The Merseysiders took the lead in the 10th minute when a Colombian James Rodriguez's smart first time pass found the Seamus Coleman who set up Dominic Calvert-Lewin to score for the third straight league game.
Palace drew level in simple fashion though with Cheikhou Kouyate heading in an Andros Townsend corner at the back post.
But five minutes before the interval, referee Kevin Friend awarded a penalty, ruling that Joel Ward had handled.
Lucas Digne had headed the ball at the Palace defender who appeared to try to pull his arm out of the way but, after being advised to check the pitchside monitor, Friend pointed to the spot and Richarlison drove home the penalty.
Hodgson was scathing of the decision and of the new interpretation of handball in general.
"I think the rule is a nonsense. I can’t understand how everyone in the game of football - the Premier League, referees, managers and coaches - have allowed this rule to come into operation. It is ruining the game of football, no question of that,” said the former England manager.
Ole Gunnar Solskjaer's United needed a penalty from Bruno Fernandes in the 100th minute of the game to take the three points back from the South coast.
Fernandes's winner, which came after referee Chris Kavanagh had initially blown for full time, concluded a match which saw Brighton hit the woodwork five times and have a penalty overturned after a VAR review, while United had a goal ruled out in each half for offside.
Brighton's Neal Maupay gave away the decisive penalty with a handball as he tried to block a late header from United captain Harry Maguire, which led to a VAR review after Kavanagh had signalled for the game to end.
Kavanagh eventually gave the penalty after consulting the pitchside VAR monitor and Fernandes lashed into the net from the spot, moments after Solly March had levelled for Brighton in the fifth minute of added time.
Brighton took a deserved lead when Maupay coolly slotted in a penalty in the 40th minute after a foul by Fernandes, but the visitors soon levelled with an own goal from Brighton defender Lewis Dunk.
A brilliant solo strike from Marcus Rashford had given United the lead in the 55th minute.
Chelsea striker Tammy Abraham struck a 93rd-minute equaliser for Frank Lampard's side after a shocking first half performance left them trailing by three goals.
An error by Marcos Alonso led to Callum Robinson opening the scoring for West Brom in the fourth minute and the Irish striker made it two when Chelsea's new signing Thiago Silva, who was given the captain's armband, sloppily was caught in possession.
Kyle Bartley was left unmarked to add a third in the 27th minute with a close-range finish to send Chelsea in three down at the break, but Mason Mount threw the Blues a lifeline with a goal 10 minutes into the second half.
Callum Hudson-Odoi made it 3-2 in the 70th minute but it took until stoppage time for Chelsea to find an equaliser when Abraham pounced on a loose ball in the box and drilled home.
Former Burnley striker Ings continued his prolific scoring for the Saints, having now netted 25 of their 54 goals since the start of last season, as he struck in the fifth minute at Turf Moor.
Kyle Walker-Peters played a superb pass through to Che Adams and, with Burnley goalkeeper Nick Pope rushing off his line, the forward squared the ball to Ings who turned it home.
(Reporting by Simon Evans; Editing by Hugh Lawson)
