Raheem Sterling was also on target as the champions claimed a convincing win in North London, with all of their goals coming inside the opening 45 minutes.
Arsenal had the first chance of the game as Gabriel Martinelli forced a good save from visiting keeper Ederson after breezing past Fernandinho.
Fernandinho made amends soon after however, as he it ran it out from the back played a superb through ball into the run of Gabriel Jesus.
Jesus created space for himself on the left of the area and cut it back to De Bruyne, who sidefooted a strike into the roof of the net from the edge of the box with just two minutes on the clock.
City were 2-0 up after quarter of an hour thanks to a wonderful team goal.
Rodri started the move on the edge of his own area and managed to pick out Phil Foden in space. Foden, who was making his second successive start in place of the injured David Silva, played it forwards to De Bruyne and the Belgian drove forward before playing a perfectly timed ball to give Sterling a tap-in.
City were out of sight with five minutes of the first half remaining as Foden played in De Bruyne, who took a few steps forward before whipping the ball into the bottom corner with his left foot before any of the Arsenal defenders could close him down.
De Bruyne could have had a hat-trick moments later but Gunners keeper Bernd Leno produced a fantastic save to tip his effort onto the post when it looked destined for the top corner.
Jesus also forced a fine save from Leno in the second half but Pep Guardiola’s men couldn’t extend their lead further, while Arsenal never looked capable of reducing the deficit.
City are third in the Premier League table and they are now 14 points behind Liverpool, who beat Watford on Saturday. Arsenal are ninth in the standings and seven points adrift of Chelsea in fourth spot.