Kevin De Bruyne, Kelechi Iheanacho, Raheem Sterling and Ilkay Gundogan gave Man City a 4-0 win over Bournemouth before Nolito was sent off.
Alexis Sanchez (2), Theo Walcott and Granit Xhaka on target for Arsenal; Slimani fired home either side of half-time for reigning champions Leicester.
Pep Guardiola's dream start to his Manchester City reign continued with an eighth win in eight matches in all competitions, a scintillating victory over Bournemouth being ignited by Kevin de Bruyne's ingenuity at the Etihad on Saturday.
The in-form Belgian scored a cheeky 15th minute freekick, deliberately firing beneath the wall of jumping defenders to set the Premier League leaders on the way to a dazzling victory which preserved their 100 percent record.
Amid some champagne football, Kelechi Iheanacho finished off a flowing team movement 10 minutes later before repaying Raheem Sterling's goal assist with the pass that enabled the England international to make it three soon after the break.
Ilkay Gundogan, on his Premier League debut, notched his first goal following more fine work from the magnificent De Bruyne, who was involved in every goal, but Nolito's needless late red card for aiming a head-butt at Adam Smith took some of the gloss from Guardiola's ideal day.
Arsenal tame 10-man Tigers 4-1
Alexis Sanchez scored twice as Arsenal easily beat 10-man Hull City, securing a third successive Premier League win for the first time since January.
Sanchez put Arsenal ahead after 17 minutes, deflecting the ball home after a Theo Walcott shot was pushed into the path of Alex Iwobi, before the hosts had Jake Livermore sent off for handball.
Sanchez's penalty was saved by Eldin Jakupovic, but Walcott doubled the lead 10 minutes into the second half when his effort was headed in by Hull defender Harry Maguire.
Hull's Robert Snodgrass pulled a goal back from the penalty spot, but Sanchez calmed any jitters in the Arsenal ranks when he rifled high into the net and Granit Xhaka rounded off the scoring with bullet finish from distance in stoppage time.
Slimani scores brace on Leicester debut
Leicester City's record buy Islam Slimani injected new life into the champions' title defence, marking his Premier League debut with his first two goals for the club in a comprehensive win.
The prolific Algerian striker, a 29.7 million pound ($38.61 million) buy from Sporting Lisbon, struck with the last action of the first half and early in the second, his two finishes demonstrating the heading prowess that had attracted manager Claudio Ranieri.
Fresh from an impressive debut in the Foxes' Champions League win in Bruges in midweek, Slimani marked his Premier League bow at the King Power by crashing home a header from a Christian Fuchs free-kick on the stroke of halftime.
Two minutes after the break, the 28-year-old nodded his second after a deflected cross from compatriot Riyad Mahrez, whose rejuvenation was also evident from the 66th minute run and cross that forced defender Ben Mee to turn an inadvertent third past his own keeper.
West Brom bash Hammers 4-2
Attacking midfielder Nacer Chadli marked a superb home debut with two goals and two assists for West Bromwich Albion as they beat hapless West Ham United 4-2 at the Hawthorns to hand the Londoners their third straight Premier League defeat.
Signed from Tottenham Hotspur for a reputed club record 13 million pounds in August, Chadli slotted home an eighth-minute penalty after Arthur Masuaku handled the ball in the box. He then set up Jose Salomon Rondon half an hour later to double the advantage.
James McClean steered home a ball from Chadli to make it 3-0 before halftime, and the 27-year-old Belgian made it four 11 minutes into the second half when he finished a counter-attack by firing Rondon's pass into the net.
Dimitri Payet mounted something of a fightback for West Ham, crossing for Michail Antonio to score and winning a penalty which Manuel Lanzini converted, but once again Slaven Bilic's side came up short as West Brom held on.