City already led 1-0 through Sergio Aguero's opener at that point and braces from Gabriel Jesus and substitute Leroy Sane completed City's biggest win over Liverpool since 1937.
City are unbeaten in 12 Premier League games, their best run under Guardiola, while Argentina striker Aguero is now the outright leading non-European goalscorer in Premier League history with 124 goals.
"After 10 v 11 it was a little bit easier for us and we played the second half the way we wanted to," said City manager Pep Guardiola.
With Liverpool having avoided defeat against their top-six rivals last season, it was the first time Jurgen Klopp's side had lost to one of their principal adversaries since a 1-0 loss at home to Manchester United in January 2016.
"The decisive decision in the whole game was the red card. I don't think it was a red card. Sadio didn't see the goalkeeper," Klopp said.
Subjected to stinging criticism following Arsenal's damaging defeats against Stoke and Liverpool, Wenger received more bad news just before kick off when it was revealed his chief transfer negotiator Dick Law has decided to step down.
Manchester City's midfielder Leroy Sane celebrates after scoring their fourth goal during the English Premier League football match against Liverpool September 9, 2017
But it took just six minutes for Danny Welbeck to lift the gloom at the Emirates Stadium as the Arsenal striker headed home from Sead Kolasinac's cross.
France forward Alexandre Lacazette doubled Arsenal's lead in the 27th minute, bagging his second goal since his pre-season move from Lyon with a curling strike from the edge of the area.
Welbeck's second goal, from Aaron Ramsey's 50th minute pass, secured Arsenal's first win since the opening weekend.
Alexis Sanchez came off the bench in the closing stages for his first Arsenal appearance this season following the collapse of his mooted move to Manchester City on transfer deadline day.
"It was a serious performance. We played well all over the pitch," Wenger said.
"Confidence is so important and the best way to get it is to perform like we did today."
Harry Kane reached his Tottenham century as the England striker's brace inspired an impressive 3-0 win at Everton.
Kane bagged his 100th Tottenham goal -- and first this season -- in the 28th minute, looping a long-range cross-shot over Everton goalkeeper Jordan Pickford.
Christian Eriksen increased Tottenham's advantage with a close-range strike in the 42nd minute after Pickford spilled a Ben Davies shot.
Kane bagged his second from Davies's 46th minute cross to kill off Everton.
"It's fantastic. It has been a crazy few years and to get the 100th goal was amazing. Hopefully I can get a few more," Kane said.
Chelsea survived a tense finish as the champions made it three successive wins with a 2-1 success at Leicester.
Arsenal's striker Danny Welbeck (R) vies with Bournemouth's defender Simon Francis (L) during the English Premier League football match September 9, 2017
Antonio Conte's side took the lead through Alvaro Morata's third goal for Chelsea as the Spain striker peeled away from Wes Morgan to meet Cesar Azpilicueta's cross with a bullet header in the 41st minute.
N'Golo Kante was a key member of Leicester's title-winning team two years ago and the Chelsea midfielder returned to haunt his old club with a 50th minute long-range strike.
Jamie Vardy gave Leicester hope in the 62nd minute when the England striker was brought down by Thibaut Courtois and picked himself up to drive home the resulting penalty.
"We must be delighted. We were in total control and could have scored more," Conte said.
"It's a good result and a good performance. After the international break it's not easy."
Brighton secured their first top-flight win for 34 years, with Pascal Gross's double clinching a 3-1 win over West Bromwich Albion at the Amex Stadium.
Watford handed Southampton manager Mauricio Pellegrino his first league defeat, 2-0 at St Mary's, thanks to goals from Abdoulaye Doucoure and Daryl Janmaat.