The first goal came from Kevin De Bruyne in the 24th minute when Jack Grealish harassed Takehiro Tomiyasu into a miscued backpass.
De Bruyne seized on the error with a perfectly weighted chip from the edge of the area that floated over the out-of-position keeper Aaron Ramsdale into the net, giving City a 1-0 lead.
Arsenal drew level three minutes before halftime, albeit in debatable fashion. As Eddie Nketiah flicked a shot goalwards from a tight angle, City keeper Ederson raced off his line and collided with the Arsenal striker just before the ball was cleared off the line by Nathan Ake.
Ederson appeared to be trying to pull out of the challenge, but Anthony Taylor awarded a penalty despite City's protests. Bukayo Saka stepped up to take the penalty and sent Ederson the wrong way with a nerveless strike, equalizing the score.
In the second half, Jack Grealish landed the vital blow when he restored the visitors' lead, scoring a deflected strike past Ramsdale in the 72nd minute.
Erling Haaland sealed the points in the 82nd minute, drilling into the far corner from De Bruyne's cross, ending the match with a 3-1 scoreline.
With this win, City demonstrated their intention to retain their Premier League title, although they are currently undergoing a difficult campaign after being charged with over 100 breaches of the financial rules by the Premier League.
This victory over title rivals Arsenal gave City a significant boost of confidence, despite having a game in hand that could tip the balance back in Arsenal's favour.
Mikel Arteta, Arsenal's manager, who had previously worked under Guardiola as his assistant, found out how hard it is for the apprentice to outwit the teacher. Guardiola has beaten Arteta in seven of their eight meetings, and this was the most significant by far.
Guardiola's men, who have won four of their last five league games, while Arsenal have stumbled with their fourth consecutive winless game in all competitions.
As the title race heats up, the match between the two teams in April could be a do-or-die showdown for both teams