Defeats for West Ham and Crystal Palace have put pressure on Slaven Bilic and Frank De Boer at the bottom of the Premier League.
Palace and West Ham are without a point after three games in a Premier League led on Saturday afternoon by unbeaten Huddersfield.
De Boer's Eagles are yet to score after a 2-0 defeat to previously winless Swansea and were booed off three matches into the Dutchman's reign.
Tammy Abraham, on loan from Chelsea, scored his first Premier League goal one minute before half-time and Jordan Ayew added a second within three minutes of the restart.
Bilic's Hammers lost 3-0 at Newcastle, who won for the first time this season through goals from Joselu, Ciaran Clark and substitute Aleksandar Mitrovic.
It was Joselu's first start for Newcastle which the Spanish striker marked by converting Christian Atsu's 36th-minute cross to lift the mood at St James' Park.
Republic of Ireland defender Clark and substitute Mitrovic sent the locals among a crowd of 52,093 home happy with second-half strikes.
Huddersfield are on seven points alongside Man City after being held to a goalless draw by Southampton.
The Terriers are still to concede a goal and lead Guardiola's men on goal difference.
Saints are also unbeaten after a second draw. 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.
Miguel Britos was sent off for a two-footed challenge on Anthony Knockaert after 24 minutes, but Brighton are still chasing a first Premier League goal this season.
They have their first point and maiden clean sheet.
Albion were unable to turn their numerical advantage into three points with Knockaert curling against the left upright midway through the first half, before Watford defender Christian Kabasele diverted the ball onto the same post before the break.