City beat Arsenal by the same scoreline in Sunday's EFL Cup final win at Wembley, giving Guardiola a first trophy after 18 months in English football.
And the runaway Premier League leaders - now 16 points clear of rivals Manchester United - blew Arsenal away before the break, becoming the first team to score three goals away to the Gunners in the first half of a Premier League match.
Arsenal made a decent start but Leroy Sane fed Bernardo Silva for a glorious opener after 15 minutes, and the Germany international was then involved in a stunning team goal as David Silva - who was on target at Wembley - added a second.
Sane scored the third before the break, finishing off another superb move, as Arsenal were regularly sliced open at a half-empty Emirates, the stadium adorned with blue lines in the snow.
Pierre-Emerick Aubameyang had a second-half penalty saved and another heavy defeat increases the growing pressure on Arsene Wenger, whose side are 10 points outside the Champions League qualification places, as sensational City close in on the title.
Henrikh Mkhitaryan urged Arsenal to "fight" for Wenger in the build-up to the game and Ederson had to save an early sighter from the Armenia international, while Vincent Kompany deflected a cross from Aaron Ramsey into the chest of City's goalkeeper.
But the visitors scored with their first meaningful attack, Bernardo Silva netting a brilliant strike.
Sane drove at the Arsenal defence with pace and skill, slipping in the Portugal international, who worked the ball on to his left foot and bent a glorious curler into Petr Cech's top-right corner.
Ederson beat away Granit Xhaka's long-range free-kick, the goalkeeper then diving to his right to cling on to a sharp Ramsey strike.
But City's clinical cutting edge sliced Arsenal open with another breathtaking attack after 27 minutes.
Sane was at the heart of it again, bamboozling Shkodran Mustafi and feeding Sergio Aguero, who laid the ball into David Silva's path. The Spain international's first touch was perfect, the second lashing a left-footed finish beyond a helpless Cech.
City were rampant, a glorious third arriving within five minutes, Sane this time on target.
Aguero's clever touch on the halfway line created acres of space in the Arsenal defence, Kevin De Bruyne sliding Kyle Walker clear to square a low cross for Sane to roll the ball home.
Nicolas Otamendi's poor challenge on Mkhitaryan offered Arsenal a lifeline shortly after the restart - the Gunners having been booed off at the break - but Ederson dived to his left to keep out Aubameyang's tame penalty.
11 - Manchester City have saved 11 of the last 19 penalties they have faced in all competitions (excludes penalty shootouts). Intimidating. pic.twitter.com/zF0ZcQeTzc — OptaJoe (@OptaJoe) March 1, 2018
With the game won before the break, City were understandably less incisive, some sloppy passing marring their second-half display, while Walker limped off with 20 minutes remaining.
Cech denied Aguero his 200th goal for the club but Guardiola could not have hoped for a more comprehensive victory to mark his City century, with Wenger left to wonder how to fix a team that has been heavily beaten three times by the league leaders this season.
Key Opta stats:
- Arsenal suffered their joint-heaviest home Premier League defeat, having also lost by three-goal margins to Coventry (1993), Middlesbrough (2001) and Chelsea (twice in 2009).
- Manchester City have now scored more Premier League goals this season (82) than they scored in the entirety of last season (80).
- This was Manchester City's biggest away win at Arsenal in any competition since a 4-0 triumph in November 1912.
- The Gunners have lost more matches in all competitions in 2018 than any other Premier League team (seven).
- Arsenal are now on their longest Premier League run without a clean sheet (10 matches) since February 2002 (11 matches).
- David Silva is only the third David to score on St. David's Day in the Premier League, after David Dunn (Blackburn v Man City in 2003) and David Luiz (Chelsea v Man Utd in 2011).
- This was the first time Arsenal conceded three goals in the first half of a home Premier League game and the first time they'd done so in a home league game since March 1989 against Nottingham Forest.