Chelsea secured their second straight win of the season and sentenced Arsenal to a second defeat with a 3-2 win in a Stamford Bridge thriller.
Marcos Alonso set up the unmarked Pedro to sidefoot past Petr Cech with nine minutes gone as Chelsea dominated and, after Pierre-Emerick Aubamayang had blazed a great chance horribly over, the home side went 2-0 up through Alvaro Morata.
But Arsenal pulled one back against the run of play 10 minutes before the break when Mkhitaryan smashed a low strike past Kepa, and minutes later Alex Iwobi steered home Henrikh Mkhitaryan's low cross to level.
Chelsea scored the all-important fifth goal with 10 minutes remaining as substitute Eden Hazard's low cross was swept home by Alonso.
Harry Kane scored his first-ever Premier League goal in August as Tottenham Hotspur beat a spirited Fulham 3-1 at Wembley.
Spurs had the better of the early stages, Lucas Moura glancing wide and Kane having a goal disallowed for a foul on Fulham keeper Fabri.
Hugo Lloris made a smart save from Tom Cairney before Spurs broke through just before half-time when Moura sent a curling shot into the corner via the inside of the post.
Fulham levelled early in the second period through Aleksandar Mitrovic, who had hit the post earlier on, but after Kane had hit the bar Kieran Trippier curled home a fine free kick -- and then England striker Kane buried a low finish to seal the points.
Richarlison continued his excellent start to life on Merseyside as Everton saw off Southampton 2-1 at Goodison Park.
The Saints could have been ahead in the early stages when Charlie Austin failed to hit the target with a header from 10 yards, and they were made to pay when Morgan Schneiderlin set up Theo Walcott for the opening goal after 15 minutes.
Southampton almost levelled when Jordan Pickford made a fine save from Danny Ings but, after Everton were forced into a change when Schneiderlin took a knock and was replaced by Tom Davies, the home side doubled their lead through Richarlison's 31st-minute header.
But with less than 10 minutes of the second half played the Saints found a way back into the match, Ings heading home unmarked to reduce the deficit.
Wolves were left to rue their luck as they hit the woodwork three times in a 2-0 defeat at Leicester.
The home side's high-tempo start was almost undone when Wolves' Joao Moutinho blasted against the bar, and with a little over 20 minutes gone they were denied again when a 20-yard Raul Jimenez strike hit the post.
But it was Leicester who went in front against the run of play when the ball cannoned in off Matt Doherty for an own goal, and Claude Puel's side doubled that lead when James Maddison scored his first goal for the club on the stroke of half-time.
Wolves made a double change at the break, Leo Bonatini and Adama Traore coming on for Diogo Jota and Helder Costa, and had a glimmer of hope after 66 minutes when Jamie Vardy was sent off for a rash challenge on Doherty before Jonny Castro hit the post.
West Ham saw familiar defensive frailties return to haunt them as they lost the lead in a 2-1 home defeat to Bournemouth.
The visitors' Callum Wilson was denied by Lukasz Fabianski, and the importance of that save became clear after 33 minutes when Javier Hernandez was brought down in the area and Marko Arnautovic stepped up to blast home from the spot for West Ham.
Fabianski made a diving save to deny David Brooks in the opening moments of the second half, but he was beaten on the hour when Wilson turned and ran at the home defence, who backed off to enable him to unleash a low strike.
Bournemouth completed the turnaround amid more weak defending from the home side, scoring their second goal in six minutes through Steve Cook's header.
Kenedy missed a 96th-minute penalty as Cardiff secured a 0-0 draw against 10-man Newcastle in their first home game back in the Premier League.
After Cardiff had enjoyed the better of the match, Newcastle appeared destined to snatch the points when Sean Morrison was adjudged to have handled in stoppage time.
But Neil Etheridge was the hero for the Bluebirds, blocking Kenedy's unconvincing spot-kick to secure a share of the spoils in a game that saw Kenneth Zohore and Harry Arter go close for Cardiff, with Ayoze Perez denied for the Magpies.